Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-10T12:12:27Z No. of bitstreams: 1 arquivototal.pdf: 955147 bytes, checksum: f6b8d3b1e6ba8fba22d9e0a28e6685fc (MD5) / Made available in DSpace on 2017-08-10T12:12:27Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 955147 bytes, checksum: f6b8d3b1e6ba8fba22d9e0a28e6685fc (MD5) Previous issue date: 2016-08-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work, we present a version little know of the famous Hölder's Inequality, considering the context of Lp and lp spaces for mixed norms. We show how a suitable use this inequality has influencied positively others classical inequalities, to highlight, the multilinear inequalities of Bohnenblust-Hille and Hardy-Littlewood. / No presente trabalho, apresentamos uma versão pouco conhecida da famosa Desigualdade de Hölder, considerando o contexto dos espaços Lp e lp com normas mistas. Mostramos como o uso adequado desta desigualdade vem influenciando positivamente outras desigualdades clássicas, a destacar, as desigualdades multilineares de Bohnenblust-Hille e Hardy-Littlewood.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-17T16:04:13Z No. of bitstreams: 1 arquivototal.pdf: 699730 bytes, checksum: d48ddf5357572db4dac922761f91c532 (MD5) / Made available in DSpace on 2017-08-17T16:04:13Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 699730 bytes, checksum: d48ddf5357572db4dac922761f91c532 (MD5) Previous issue date: 2016-04-04 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this study we show two classical inequalities, namely Bohnenblust-Hille inequality and Hardy-Littlewood inequality. The rst one, conceived as a tool for the study of problems related to Dirichlet series, is a generalization of Littlewood`s 4/3 inequality to multilinear forms. The second is a generalization of Bohnenblust-Hille inequality, produced by the replacement of c0 with lp. / No presente trabalho abordaremos duas desigualdades cl assicas, a saber, a Desigualdade de Bohnenblust-Hille e a Desigualdade de Hardy- Littlewood. A primeira, surgiu como ferramenta para o estudo de problemas relacionados a s eries de Dirichlet e e uma generaliza c~ao para formas multilineares da Desigualdade 4/3 de Littlewood. A segunda consiste de uma generaliza c~ao da Desigualdade de Bohnenblust-Hille, produzida pela substituição de c0 por lp.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-23T16:38:50Z No. of bitstreams: 1 arquivototal.pdf: 1943524 bytes, checksum: 935ea8764b03a0cab23d8c7c772a137d (MD5) / Made available in DSpace on 2017-08-23T16:38:50Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1943524 bytes, checksum: 935ea8764b03a0cab23d8c7c772a137d (MD5) Previous issue date: 2016-03-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work is divided into three parts. In the first part, we investigate the behavior of the constants of the Bohnenblust–Hille and Hardy–Littlewood polynomial and multilinear inequalities. In the second part, we show an optimal spaceability result for a set of non-multiple summing forms on `p and we also generalize a result related to cotype (from 2010) as highlighted by G. Botelho, C. Michels, and D. Pellegrino. Moreover, we prove new coincidence results for the class of absolutely and multiple summing multilinear operators (in particular, we show that the well-known Defant–Voigt theorem is optimal). Still in the second part, we show a generalization of the Bohnenblust–Hille and Hardy–Littlewood multilinear inequalities and we present a new class of summing multilinear operators, which recovers the class of absolutely and multiple summing operators. In the third part, it is proved the existence of large algebraic structures inside, among others, the family of Lebesgue measurable functions that are surjective in a strong sense, the family of non-constant di↵erentiable real functions vanishing on dense sets, and the family of noncontinuous separately continuous real functions. / Este trabalho est´a dividido em trˆes partes. Na primeira parte, investigamos o comportamento das constantes das desigualdades polinomial e multilinear de Bohnenblust–Hille e Hardy–Littlewood. Na segunda parte, mostramos um resultado ´otimo de espa¸cabilidade para o complementar de uma classe de operadores m´ultiplo somantes em `p e tamb´em generalizamos um resultado relacionado a cotipo (de 2010) devido a G. Botelho, C. Michels e D. Pellegrino. Al´em disso, provamos novos resultados de coincidˆencia para as classes de operadores multilineares absolutamente e m´ultiplo somantes (em particular, mostramos que o famoso teorema de Defant–Voigt ´e ´otimo). Ainda na segunda parte, mostramos uma generaliza¸c˜ao das desigualdades multilineares de Bohnenblust–Hille e Hardy–Littlewood e apresentamos uma nova classe de operadores multilineares somantes, a qual recupera as classes dos operadores multilineares absolutamente e m´ultiplo somantes. Na terceira parte, provamos a existˆencia de grandes estruturas alg´ebricas dentro de certos conjuntos, como, por exemplo, a fam´ılia das fun¸c˜oes mensur´aveis `a Lebesgue que s˜ao sobrejetivas em um sentido forte, a fam´ılia das fun¸c˜oes reais n˜ao constantes e diferenci´aveis que se anulam em um conjunto denso e a fam´ılia das fun¸c˜oes reais n˜ao cont´ınuas e separadamente cont´ınuas.