We give a systematic study of the Hardy spaces of functions with values in the non-commutative Lp-spaces associated with a semifinite von Neumann algebra M. This is motivated by matrix valued harmonic analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of non-commutative martingale inequalities. Our non-commutative Hardy spaces are defined by non-commutative Lusin integral functions. It is proved in this dissertation that they are equivalent to those defined by the non-commutative Littlewood-Paley G-functions. We also study the Lp boundedness of operator valued dyadic paraproducts and prove that their Lq boundedness implies their Lp boundedness for all 1 < q < p < ∞.

This thesis will present new results involving Hardy and Hardy-Sobolev-Maz'ya inequalities for fractional integrals. There are two key ingredients to many of these results. The first is the conformal transformation between the upper halfspace and the unit ball. The second is the pseudosymmetric halfspace rearrangement, which is a type of rearrangment on the upper halfspace based on Carlen and Loss' concept of competing symmetries along with certain geometric considerations from the conformal transformation. After reducing to one dimension, we can use the conformal transformation to prove a sharp Hardy inequality for general domains, as well as an improved fractional Hardy inequality over convex domains. Most importantly, the sharp constant is the same as that for the halfspace. Two new Hardy-Sobolev-Maz'ya inequalities will also be established. The first will be a weighted inequality that has a strong relationship with the pseudosymmetric halfspace rearrangement. Then, the psuedosymmetric halfspace rearrangement will play a key part in proving the existence of the standard Hardy-Sobolev-Maz'ya inequality on the halfspace, as well as some results involving the existence of minimizers for that inequality.

Sarason a décrit les sous-espaces fermés réduisants (invariants par $S$, opérateur de multiplication par $z$, et par $S^*$) et<br />doublement-invariants (invariants par $S$ et $S^{-1}$) de l'espace de Hardy $H^2(A)$ où $A$ est un anneau. Nous établissons les versions vectorielles.<br /><br /> Nous donnons aussi la version vectorielle d'un résultat de Hitt<br />portant sur les sous-espaces $S^{*}-$faiblement<br />invariants via l'étude des contractions perturbées par des opérateurs de<br />rang fini.\\<br /><br />Dans la seconde partie, nous étudions les bases de<br />noyaux reproduisants sur les espaces de De Branges--Rovnyak, au moyen du modèle de Sz-nagy--Foias. <br />Le dernier problème présenté est de caractériser les opérateurs $T\in \LL(\HH)$ complexes symétriques. Nous en donnons des classes d'exemples.

Dissertation--Marburg--Universität, 2003. / Bibliogr. p. 255-273.

Texte remanié de : Thèse de doctorat : ? : University of Illinois, Urbana-Champaign : 1989-96. / Bibliogr. p. 207-219. Index.

Thesis (M.A.)--Kutztown University of Pennsylvania, 1999. / Source: Masters Abstracts International, Volume: 45-06, page: 2823. Typescript. Abstract precedes thesis as, preliminary leaves [2-3]. Includes bibliographical references (leaves 109-112).

Thesis (Ph. D.)--Florida State University, 2004. / Advisor: Dr. Daniel M. Oberlin, Florida State University, College of Arts and Sciences, Dept. of Mathematics. Title and description from dissertation home page (June 18, 2004). Includes bibliographical references.

No description available.

So many critics have pointed to George Eliot as a symbol of the nineteenth century's religious flux that the idea is becoming a commonplace one. House, for example, in "Qualities of George Eliot's Unbelief", concedes that Eliot is not a typical Victorian, "Yet her history her intellectual and spiritual and moral history -- exemplifies so many trends and qualities of Victorian thought that she deserves to be considered alone." [...]

In an unpublished study in Toronto it was observed that cases were in Hardy-Weinberg Equilibrium at a locus whereas their family members were in Hardy-Weinberg Disequilibrium (HWD). This led to an investigation of relatives of affected individuals to see whether the multiplicative model could be revealed by a nonzero HWD coefficient in relatives. Genotypic frequencies and HWD coefficients were derived for affected individuals and their affected and unaffected relatives. Methods were also developed to test for association using data from affected individuals and their relatives. In addition, a model was developed to assess whether the HWD observed in a data set from a stratified population can be explained by both genetic association and stratification. Parameter estimates for these models can be obtained using maximum likelihood methods, and used to deduce the mode of inheritance of the disease. / Departure from HWE (HWD) in a sample may indicate genotyping error, population stratification, selection bias, or some combination thereof. Therefore, loci exhibiting HWD are often excluded from association studies. However, it has been shown that in case-control studies HWD can result from a genetic effect at the locus, and HWD at a marker locus can be interpreted as evidence for association with a disease. In an unpublished study in Toronto it was observed that cases were in Hardy- Weinberg equilibrium at a locus whereas their family members were in HWD. It has been shown that the HWD coefficient for a multiplicative genetic model is zero. This led to an investigation of relatives of affected individuals to see whether the multiplicative model could be revealed by a nonzero HWD coefficient in relatives. Genotypic frequencies and HWD coefficients were derived for affected individuals and their affected and unaffected relatives. A substantial HWD was found in both individuals in dominant and recessive genetic models but HWD is only slightly nonzero for additive and multiplicative models. Methods were also developed to test for association using data from affected individuals and their relatives. Parameter estimates for these models can be obtained using maximum likelihood methods, and estimates provide valuable information regarding the mode of inheritance of the disease. The methods were applied to 112 discordant sib pairs with Alzheimer’s disease typed for the ApoE polymorphism and a significant association was observed between the "4 ApoE allele and Alzheimer’s disease. Case-control studies may indicate spurious association with a marker locus in a stratified population. Methods were developed to determine if the HWD observed in a data set from a stratified population can be explained by both genetic association and stratification. Parameter estimates for these models can be obtained using maximum likelihood methods, and used to deduce the mode of inheritance of the disease. Applying the model to the R990G SNP of the CASR gene, it was found that the HWD was adequately explained by a recessive genetic association and a stratification proportion of 10%, consistent with the population of Toronto.