This dissertation studies a number of issues related to Development Economics. The first chapter explains how we can use multiple correspondence analysis to calculate an asset index, and then offers an inequality analysis using the asset index. The second chapter provides a theoretical explanation of an odd relationship between child labor and per capita land holding in a household, and then provides empirical evidence for the explanation. Finally, the third chapter represents the results of a study of the behavior of rural households during shocks. Across the entire dissertation, we use three cross sectional surveys, conducted in 2001, 2007-8 and 2010-11 in Zimbabwe. / Ph. D. / In chapter 1, we explain an alternative for measuring household wealth to conduct poverty and inequality analysis in cases in which data on income and consumption expenditures are not available, are difficult to collect, or the data suffer from a large amount of mis-measurement. In chapters 2 and 3 we study child labor, defined based on school attendance, in rural areas of the Zimbabwe. As reductions in child labor result in more educational attainment which is associated with higher economic growth, it is valuable to identify factors associated with use of child labor. In chapter 2, we show that both very poor households (poor based on land holdings) and households with medium-sized holdings are likely to have a high incidence of child labor. Policy makers wishing to reduce child labor should focus on both classes of households. The latter group would be excluded if poverty were thought to be the sole cause of child labor. It is even possible that small land holders might be less likely to send their children to work than households whose land holding is in an intermediate range. Intuition might say that rural children are put to work more during negative shocks (e.g. macroeconomic crisis, price fall in agricultural products, drought, pest attack, etc) and less during positive shocks in comparison to normal conditions. But we show in chapter 3 that children might be pulled out of schools during positive shocks and inverse during negative shocks in Zimbabwe, so policy makers should be worried during positive shocks and they may lower costs of education and increase incentives for keeping children in school during positive shocks by providing voucher programs and subsidies to the school.

In this dissertation, I study the role of local markets and firms in explaining labor market inequality across genders, and across workers. My results show that local labor markets have a relevant role in accounting for differences in labor market outcomes across genders. The dissertation is structured in three chapters, each containing a stand-alone paper. In the first chapter I show large and persistent differences exist in women’s labor force participation within multiple countries. These persistent differences in employment can arise if where women grow up shapes their work choices. However, they can also arise under endogenous sorting, so that women who want to work move to places where more women work. In this chapter, I use rich data from Indonesia to argue that the place women grow up in shapes their participation in the labor market as adults. To do so, I leverage variation coming from women moving across labor markets to estimate the effect on women’s labor force participation of spending more time in their birthplace. My strategy is similar to that of Chetty and Hendren (2018) and compares the labor supply choices of women who currently live in the same location, but who emigrated from their birthplace at different ages. My results indicate that birthplace has strong and persistent effects on adult women’s labor supply. By the time they turn sixteen, women born in a location at the 75th percentile of female employment will be 5 percentage points more likely to work than those born in a 25th percentile location. Place is particularly important during the formative period between 9 and 16 years old. These results suggest that between 23 percent of the current spatial inequality in women’s employment is transmitted to the next generation growing up in these locations. The second chapter studies the relationship between city size and gender inequality in the United States. It is well known that living in a larger cities is associated with a wage premium, but there is growing evidence that this premium has declined since the 1980s. (Autor, 2019). In this paper, I use data from U.S. Commuting Zones for the period between 1970 and 2020 to document that the decline in the urban wage premium affected men and women differently. While women were relatively isolated from the premium decline, men with lower education experienced the brunt of the impact. This caused a large relative increase in the urban wage premium for women: it went from being on par with the urban premium for men to being 44% larger in 2016. I argue that these differential trends result from a combination of gender specialization and the evolution of urban skill premiums. Urban premiums declined the most in those skills men without a college degree use more intensively. Finally, the third chapter I study the role of universities in explaining earnings inequality in U.S. academia. Previous applications from the Abowd, Kramarz, and Margolis (1990) method –AKM– found that the best firms pay workers over and above their own productivity. These firm rents contribute to overall wage inequality. In this paper, we apply the AKM model to measure whether there are significant firm (university/college) effects on faculty earnings in academia. We apply the model to measure the pecuniary rents associated with working as tenure-track faculty at a more prestigious university or college in the United States. To do so, we take advantage of matched employer-employee data from the Survey of Doctorate Recipients. We find little evidence of pecuniary university premiums in the most prestigious US academic institutions. Once we control for urbanicity, the effect of university/college rankings on institutions’ fixed-effects on earnings is statistically insignificant and sufficiently precisely measured that we can rule out anything larger than modest effects.

Yes / In England, social choice in education faces trade-offs between equity and efficiency. The scope of these trade-offs ranges from the introduction of choice to correcting 'market failures' to reduce inequalities and restrict social injustices. The article analyses the English school education system and its relationship with social preferences. The authors argue that the moral and legal need for non-discriminatory education supersedes perceptions of cost-effectiveness and utilitarianism. They consider that the current system has failed owing to inappropriate processes within social and public choice and that a reformed system based on a social democratic imperative will allow closer social integration on the basis of ability rather than privilege.

Despite considerable research efforts, the relationship between inequality and demand for redistribution remains a highly contested topic within comparative political economy. This paper argues that a central yet widely overlooked mechanism linking macro-level income inequality to preferences for redistribution has to with the micro-level implications of certain externalities of inequality. Focusing on fear of crime, as one such externality, I argue that because (i) in- equality and crime are positively related, and (ii) because crime and fear of crime have a negative effect in individual utility, it follows that increasing in- equality should have a positive effect on support for redistribution. Importantly, however, the argument of this paper also recognises that redistribution is but one of several means through which a concern about crime can be addressed, with the most relevant alternatives being increased policing and harsher punitive measures. Drawing on literatures in criminology and political sociology, I theorise that a key determinant of this choice | between redistribution and policing/punishment as alternative approaches to dealing with crime | is the level of ethnic heterogeneity in the population. Taken together, therefore, this paper's argument implies that inequality will have differential effects on support for redistribution in different contexts: in cases where the population is homogenous, fear of crime - and by consequence inequality - will boost demand for redistribution, whilst no such effects will follow in contexts of high heterogeneity. Using a two-step statistical methodology, I analyse Eurobarometer and ESS data from 21 OECD countries and find persuasive empirical support for my theoretical expectations. Fear of crime is more strongly associated to support for redistribution when the level of population heterogeneity remains low, whilst the opposite holds true for the relationship between fear of crime and support for policing and punishment.

This thesis deals with the determinants and mechanisms of individual secularisation processes in a cross-national perspective. In this ‘collected volume’ of six stand-alone articles, I examine religious beliefs and behaviours as well as attitudes towards religion and politics, whereby the validity of the main theories of religious change (classical secularisation theory, existential security hypothesis, supply-side explanations, historical/cultural approaches and conflict theories) are put to an empirical test. The main conclusion is that the fundamental mechanisms suggested by secularisation theories are valid and that we can identify main determinants of religiosity worldwide. However, only a combination of existing approaches is capable of explaining a broad range of the phenomena observed. Chapter 1 (co-authored with Nan Dirk de Graaf and Peter Schmidt) deals with the fundamental mechanisms that facilitate the socialisation of religious beliefs. Under conditions of high inequality, religion acts as a source of social capital that benefits the religious socialisation of individuals outside of the family context. If levels of inequality fall, this ‘social value of religion’ is diminished and religious socialisation depends more strongly on parental efforts, thereby gradually leading to intergenerational secularisation. In Chapter 2 (co-authored with Anja Neundorf) we show that the state in Eastern Europe played a crucial role in de-establishing as well as re-establishing religious plausibility structures, which explains lower levels of religious belief in Cold War cohorts as well as the religious revival after the end of the Cold War. Chapters 3 and 4 examine the topic of religion and politics and the mechanisms behind the support for the 9/11 attacks in the Muslim world. Levels of existential security and income inequality have a strong impact on the preferences for religious politicians in a cross-sectional as well as in a longitudinal perspective. Moreover, religiosity and altruistic behaviour run the risk of being converted into pro-terrorist support under conditions of high levels of inequality and low development levels. The final two chapters show that –in a world-wide comparison development levels, inequality and the Socialist history of countries explain 75% of the variation in religiosity between countries. Furthermore, future developments in religious change will also be subject to changes in fertility. The main drivers of secularisation processes can be identified, but for the majority of the world population these conditions are not met at present, nor will they be met in the near future.

This paper examines the effect of governance on inequality, specifically if improvements in the World Bank’s Worldwide Governance Indicators affect inequality as measured by two Gini coefficients: Market Gini, before taxes and redistribution, and Net Gini, after taxes and redistribution. The data for the Gini measurements was taken from the Standardized World Income Inequality Database (SWIID) and the data for the Worldwide Governance Indicators was taken from the World Bank. Data for fifteen (15) years, from the start of the Worldwide Governance Indicators until 2013, was combined with data from SWIID for the same years. In all, data from one hundred fifty-six (156) countries with a full set of six (6) indicators for the years that had at least one corresponding Gini measurements were used in this study: in total one thousand seven hundred and forty-seven (1747) observations. In a pooled OLS regression, controlling for growth with the variable GDP per Capita expressed as a per cent (%) change on an annual basis, the individual indicators gave the following results, where a positive sign indicates increased inequality and vice versa: Control of Corruption and Regulatory Quality showed a positive sign for both Gini measurements. Rule of Law, Government Effectiveness, Political Stability and the Absence of Violence/Terrorism, gave a negative sign for both Gini measurements. Voice and Accountability showed a positive sign for Market Gini and a negative sign for Net Gini. The fact that an improvement in Control of Corruption increased inequality both before and after taxes and redistribution was unexpected and should be further researched.

O presente estudo tem como objetivo testar o argumento de que as escolas públicas modificaram a sua estratégia educacional ao buscar o aumento do seu Índice de Desenvolvimento da Educação Básica (IDEB) após 2007 (ano da criação desse índice). A base do argumento é que essa mudança de estratégia foi no sentido de alocar maiores investimentos e esforços educacionais nos alunos com as melhores chances de apresentarem os maiores ganhos de proficiência na Prova Brasil, o que poderia aumentar a desigualdade de proficiência dentro das escolas. Os nossos resultados indicam evidências para rejeitar esse argumento inicial. Há evidências de que as escolas, que aumentaram o IDEB entre 2007 e 2009, reduziram a desigualdade de proficiência dos seus alunos. Além disso, existem evidências de que a desigualdade entre diferentes escolas pode estar aumentando. / The present study aims to test our argument that public schools changed their educational strategies while trying to increase their IDEB (educational quality index) between 2007 and 2009. This argument is about an increase in the educational investments and efforts from schools into their students, specifically those that presented the highest chances to obtain the largest achievement gains. These investments and efforts would contribute to increase the achievement inequality within schools. Ours results shows evidence to reject our argument. There is evidence that these schools contributed to lower the achievement inequality between their students. We also find evidence that achievement inequality may be increasing between schools.

O objetivo principal do presente trabalho foi analisar a estrutura e os condicionantes da desigualdade socioeducacional no Tocantins enquanto um dos determinantes do comportamento da desigualdade regional. Dessa forma, tem a intenção de desenvolver, de forma empírica e conceitual, uma abordagem das relações originais entre educação e desigualdade regional. Além disso, o presente estudo elabora um novo indicador sintético e analítico denominado Índice de Desigualdade Socioeducacional (Idsed), que parte da compreensão de que as relações sociais de produção capitalista são desiguais e projetam tais desigualdades, próprias das condições de acesso ao mercado, na estruturação das escolas, de acordo com os bens materiais e simbólicos que dispõem os beneficiários desse serviço. O caminho percorrido da pesquisa passa pelo crivo da discussão sobre o conceito de região que permeia a Geografia, ligando a uma reflexão sobre globalização, desenvolvimento e desigualdade em contextos regionais. A seguir, discute sobre os indicadores socioeconômicos, fazendo um panorama do desempenho dos indicadores socioeconômicos no Brasil e no Tocantins, além de analisar indicadores educacionais ligados às séries históricas das taxas de transição do ensino fundamental. Finalmente, a cartografia da desigualdade socioeducacional tocantinense é mostrada diante das condições socioeconômicas, socioculturais, infraestruturais e educacionais que permeiam o universo escolar tocantinense através do Idsed. / This research aims to analyze the structure and constraints of the socio educational inequality in Tocantins as one of the determinants of regional inequality behavior. Therefore, it intends to develop an empirical and conceptual way, an approach of the original relations between education and regional inequality. In addition, this research develops a new synthetic and analytical indicator called Socio Education Inequality Index (SEII), in which part of the realization that the social relations of capitalist production are unequal and designed such inequalities, own market access conditions, in the school structuring according to the symbolic and material goods that are available to service’s beneficiaries. The way we in which conduct our research was through of discussions about the region's concept that pervade the Geography, relating to globalization reflection, development and inequality in regional contexts. Then, we discuss the socioeconomic indicators, making an overview of socioeconomics development in Brazil and Tocantins. We also analyze education indicators linked to historical series of transition’s rates from elementary school. Finally, the socio educational inequality’s mapping is presented in front of the socio-economic, socio-cultural, infrastructural and educational conditions which pervade the tocantinense school universe through of Socio Educational Inequality Index.

<p>This thesis treats inequalities of Carlson type, i.e. inequalities of the form</p><p><mml:math><mml:semantics><mml:mrow><mml:mrow><mml:msub><mml:mi>∥f∥</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mo mml:stretchy="false">≤</mml:mo><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∏</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msubsup><mml:mi>∥f∥</mml:mi><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:msub><mml:mo mml:stretchy="false">θ</mml:mo><mml:mi>i</mml:mi></mml:msub></mml:msubsup></mml:mrow></mml:mrow></mml:semantics></mml:math></p><p>where <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mo mml:stretchy="false">θ</mml:mo><mml:mn>i </mml:mn></mml:msub></mml:mrow><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:semantics></mml:math> and <i>K</i> is some constant, independent of the function <i>f</i>. <i>X</i> and <mml:math><mml:semantics><mml:msub><mml:mi>A</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:semantics></mml:math> are normed spaces, embedded in some Hausdorff topological vector space. In most cases, we have <mml:math><mml:semantics><mml:mrow><mml:mi>m</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:semantics></mml:math>, and the spaces involved are weighted Lebesgue spaces on some measure space. For example, the inequality</p><p><mml:math><mml:semantics><mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∫</mml:mo><mml:mn>0</mml:mn><mml:mo mml:stretchy="false">∞</mml:mo></mml:munderover><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi mml:fontstyle="italic">dx</mml:mi><mml:mo mml:stretchy="false">≤</mml:mo><mml:msqrt><mml:mo mml:stretchy="false">π</mml:mo></mml:msqrt></mml:mrow><mml:msup><mml:mfenced mml:open="(" mml:close=")"><mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∫</mml:mo><mml:mn>0</mml:mn><mml:mo mml:stretchy="false">∞</mml:mo></mml:munderover><mml:msup><mml:mi>f</mml:mi><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow></mml:mfenced><mml:mrow><mml:mn>1</mml:mn><mml:mo mml:stretchy="false">/</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msup><mml:msup><mml:mfenced mml:open="(" mml:close=")"><mml:mrow><mml:mrow><mml:munderover><mml:mo mml:stretchy="false">∫</mml:mo><mml:mn>0</mml:mn><mml:mo mml:stretchy="false">∞</mml:mo></mml:munderover><mml:msup><mml:mi>x</mml:mi><mml:mn>2 </mml:mn></mml:msup></mml:mrow><mml:msup><mml:mi>f</mml:mi><mml:mn>2 </mml:mn></mml:msup><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow></mml:mfenced><mml:mrow><mml:mn>1</mml:mn><mml:mo mml:stretchy="false">/</mml:mo><mml:mn>4</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:semantics></mml:math></p><p>first proved by F. Carlson, is the above inequality with <mml:math><mml:semantics><mml:mrow><mml:mi>m</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:semantics></mml:math>, <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:msub><mml:mo mml:stretchy="false">θ</mml:mo><mml:mn>1 </mml:mn></mml:msub><mml:mo mml:stretchy="false">=</mml:mo><mml:msub><mml:mo mml:stretchy="false">θ</mml:mo><mml:mn>2 </mml:mn></mml:msub></mml:mrow><mml:mo mml:stretchy="false">=</mml:mo><mml:mfrac><mml:mn>1 </mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:mrow></mml:semantics></mml:math>, <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:mi>X</mml:mi><mml:mo mml:stretchy="false">=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mo mml:stretchy="false">ℝ</mml:mo><mml:mrow><mml:mo mml:stretchy="false">+</mml:mo><mml:mn>, </mml:mn></mml:mrow></mml:msub><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow><mml:mn>, </mml:mn><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>1 </mml:mn></mml:msub><mml:mo mml:stretchy="false">=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn>2 </mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mo mml:stretchy="false">ℝ</mml:mo><mml:mrow><mml:mo mml:stretchy="false">+</mml:mo><mml:mn>, </mml:mn></mml:mrow></mml:msub><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:semantics></mml:math> and <mml:math><mml:semantics><mml:mrow><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mn>2 </mml:mn></mml:msub><mml:mo mml:stretchy="false">=</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mn>2 </mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mo mml:stretchy="false">(</mml:mo><mml:mrow><mml:msub><mml:mo mml:stretchy="false">ℝ</mml:mo><mml:mrow><mml:mo mml:stretchy="false">+</mml:mo><mml:mn>, </mml:mn></mml:mrow></mml:msub><mml:msup><mml:mi>x</mml:mi><mml:mn>2 </mml:mn></mml:msup><mml:mi mml:fontstyle="italic">dx</mml:mi></mml:mrow><mml:mo mml:stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:semantics></mml:math>. In different situations, suffcient, and sometimes necessary, conditions are given on the weights in order for a Carlson type inequality to hold for some constant <i>K</i>. Carlson type inequalities have applications to e.g. moment problems, Fourier analysis, optimal sampling, and interpolation theory.</p>

This thesis treats inequalities of Carlson type, i.e. inequalities of the form &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;∥f∥&lt;/mml:mi&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;/mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;≤&lt;/mml:mo&gt;&lt;mml:mi&gt;K&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:munderover&gt;&lt;mml:mo mml:stretchy="false"&gt;∏&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;mml:mi&gt;m&lt;/mml:mi&gt;&lt;/mml:munderover&gt;&lt;mml:msubsup&gt;&lt;mml:mi&gt;∥f∥&lt;/mml:mi&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;A&lt;/mml:mi&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:msub&gt;&lt;mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;θ&lt;/mml:mo&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:msub&gt;&lt;/mml:msubsup&gt;&lt;/mml:mrow&gt;&lt;/mml:mrow&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt; where &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:munderover&gt;&lt;mml:mo mml:stretchy="false"&gt;∑&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;mml:mi&gt;m&lt;/mml:mi&gt;&lt;/mml:munderover&gt;&lt;mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;θ&lt;/mml:mo&gt;&lt;mml:mn&gt;i &lt;/mml:mn&gt;&lt;/mml:msub&gt;&lt;/mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt; and K is some constant, independent of the function f. X and &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;A&lt;/mml:mi&gt;&lt;mml:mi&gt;i&lt;/mml:mi&gt;&lt;/mml:msub&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt; are normed spaces, embedded in some Hausdorff topological vector space. In most cases, we have &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;m&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt;, and the spaces involved are weighted Lebesgue spaces on some measure space. For example, the inequality &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:munderover&gt;&lt;mml:mo mml:stretchy="false"&gt;∫&lt;/mml:mo&gt;&lt;mml:mn&gt;0&lt;/mml:mn&gt;&lt;mml:mo mml:stretchy="false"&gt;∞&lt;/mml:mo&gt;&lt;/mml:munderover&gt;&lt;mml:mi&gt;f&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi mml:fontstyle="italic"&gt;dx&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;≤&lt;/mml:mo&gt;&lt;mml:msqrt&gt;&lt;mml:mo mml:stretchy="false"&gt;π&lt;/mml:mo&gt;&lt;/mml:msqrt&gt;&lt;/mml:mrow&gt;&lt;mml:msup&gt;&lt;mml:mfenced mml:open="(" mml:close=")"&gt;&lt;mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:munderover&gt;&lt;mml:mo mml:stretchy="false"&gt;∫&lt;/mml:mo&gt;&lt;mml:mn&gt;0&lt;/mml:mn&gt;&lt;mml:mo mml:stretchy="false"&gt;∞&lt;/mml:mo&gt;&lt;/mml:munderover&gt;&lt;mml:msup&gt;&lt;mml:mi&gt;f&lt;/mml:mi&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:msup&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mi mml:fontstyle="italic"&gt;dx&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:mfenced&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;mml:mo mml:stretchy="false"&gt;/&lt;/mml:mo&gt;&lt;mml:mn&gt;4&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msup&gt;&lt;mml:msup&gt;&lt;mml:mfenced mml:open="(" mml:close=")"&gt;&lt;mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:munderover&gt;&lt;mml:mo mml:stretchy="false"&gt;∫&lt;/mml:mo&gt;&lt;mml:mn&gt;0&lt;/mml:mn&gt;&lt;mml:mo mml:stretchy="false"&gt;∞&lt;/mml:mo&gt;&lt;/mml:munderover&gt;&lt;mml:msup&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;mml:mn&gt;2 &lt;/mml:mn&gt;&lt;/mml:msup&gt;&lt;/mml:mrow&gt;&lt;mml:msup&gt;&lt;mml:mi&gt;f&lt;/mml:mi&gt;&lt;mml:mn&gt;2 &lt;/mml:mn&gt;&lt;/mml:msup&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;(&lt;/mml:mo&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mi mml:fontstyle="italic"&gt;dx&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;/mml:mfenced&gt;&lt;mml:mrow&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;mml:mo mml:stretchy="false"&gt;/&lt;/mml:mo&gt;&lt;mml:mn&gt;4&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msup&gt;&lt;/mml:mrow&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt; first proved by F. Carlson, is the above inequality with &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;m&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt;, &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;θ&lt;/mml:mo&gt;&lt;mml:mn&gt;1 &lt;/mml:mn&gt;&lt;/mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;θ&lt;/mml:mo&gt;&lt;mml:mn&gt;2 &lt;/mml:mn&gt;&lt;/mml:msub&gt;&lt;/mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:mfrac&gt;&lt;mml:mn&gt;1 &lt;/mml:mn&gt;&lt;mml:mn&gt;2&lt;/mml:mn&gt;&lt;/mml:mfrac&gt;&lt;/mml:mrow&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt;, &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mi&gt;X&lt;/mml:mi&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;L&lt;/mml:mi&gt;&lt;mml:mn&gt;1&lt;/mml:mn&gt;&lt;/mml:msub&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;(&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;ℝ&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;+&lt;/mml:mo&gt;&lt;mml:mn&gt;, &lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mi mml:fontstyle="italic"&gt;dx&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;mml:mn&gt;, &lt;/mml:mn&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;A&lt;/mml:mi&gt;&lt;mml:mn&gt;1 &lt;/mml:mn&gt;&lt;/mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;L&lt;/mml:mi&gt;&lt;mml:mn&gt;2 &lt;/mml:mn&gt;&lt;/mml:msub&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;(&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;ℝ&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;+&lt;/mml:mo&gt;&lt;mml:mn&gt;, &lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:mi mml:fontstyle="italic"&gt;dx&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;/mml:mrow&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt; and &lt;mml:math&gt;&lt;mml:semantics&gt;&lt;mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;A&lt;/mml:mi&gt;&lt;mml:mn&gt;2 &lt;/mml:mn&gt;&lt;/mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;=&lt;/mml:mo&gt;&lt;mml:msub&gt;&lt;mml:mi&gt;L&lt;/mml:mi&gt;&lt;mml:mn&gt;2 &lt;/mml:mn&gt;&lt;/mml:msub&gt;&lt;/mml:mrow&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;(&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:msub&gt;&lt;mml:mo mml:stretchy="false"&gt;ℝ&lt;/mml:mo&gt;&lt;mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;+&lt;/mml:mo&gt;&lt;mml:mn&gt;, &lt;/mml:mn&gt;&lt;/mml:mrow&gt;&lt;/mml:msub&gt;&lt;mml:msup&gt;&lt;mml:mi&gt;x&lt;/mml:mi&gt;&lt;mml:mn&gt;2 &lt;/mml:mn&gt;&lt;/mml:msup&gt;&lt;mml:mi mml:fontstyle="italic"&gt;dx&lt;/mml:mi&gt;&lt;/mml:mrow&gt;&lt;mml:mo mml:stretchy="false"&gt;)&lt;/mml:mo&gt;&lt;/mml:mrow&gt;&lt;/mml:mrow&gt;&lt;/mml:semantics&gt;&lt;/mml:math&gt;. In different situations, suffcient, and sometimes necessary, conditions are given on the weights in order for a Carlson type inequality to hold for some constant K. Carlson type inequalities have applications to e.g. moment problems, Fourier analysis, optimal sampling, and interpolation theory.