Hui, Chun Yin. / On t.p. "n" is a superscript. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 80-83). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Basic properties of real hypersurfaces in CN --- p.9 / Chapter 2.1 --- Hypersurfaces in CN and some nondegeneracy conditions --- p.9 / Chapter 2.2 --- CR functions and their holomorphic extensions --- p.15 / Chapter 2.3 --- Normal coordinates for real analytic hypersurfaces --- p.18 / Chapter 3 --- The algebraic results for reflection principle --- p.22 / Chapter 4 --- Reflection principle for real analytic hypersurfaces in higher complex dimensions --- p.30 / Chapter 4.1 --- Reflection principle for Levi nondegenerate hypersurfaces --- p.31 / Chapter 4.2 --- Essentially finite real analytic hypersurfaces and not totally degenerate CR mappings --- p.38 / Chapter 4.3 --- Reflection principle for essentially finite hypersurfaces --- p.44 / Chapter 4.4 --- Reflection principle for CR mappings and bounded domains --- p.54 / Chapter 4.5 --- Futher results on the reflection principle --- p.64 / Chapter 5 --- An extension result of CR functions by a general Schwarz reflection principle --- p.66 / Chapter 5.1 --- A general Schwarz reflection principle --- p.66 / Chapter 5.2 --- "Holomorphic extension of CR functions on a real analytic, generic CR submanifold in CN" --- p.69 / Bibliography --- p.80

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

by Yeung Chung Kuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 104-105). / Chapter 1 --- Infinitesimal Deformation of Compact Complex Manifolds --- p.3 / Chapter 1.1 --- Differentiable Family --- p.3 / Chapter 1.2 --- Infinitesimal Deformation in Differentiable Family --- p.6 / Chapter 1.3 --- Trivial Differentiable Family --- p.8 / Chapter 1.4 --- Complex Analytic Family --- p.13 / Chapter 1.5 --- Induced Family --- p.19 / Chapter 2 --- Theorem of Existence --- p.22 / Chapter 2.1 --- Introduction --- p.22 / Chapter 2.2 --- "Some Facts on the qth Cohomology Group Hq(M,´ة）" --- p.23 / Chapter 2.3 --- Obstructions to Deformation --- p.24 / Chapter 2.4 --- An Elementary Method for Theorem of Existence --- p.26 / Chapter 2.5 --- Proof of Theorem of Existence --- p.35 / Chapter 3 --- "Comparison between the Number of Moduli m(M) and dim H1 (M,´ة）" --- p.64 / Chapter 3.1 --- Number of Moduli of Compact Complex Manifold --- p.64 / Chapter 3.2 --- Examples --- p.68 / Chapter 4 --- Theorem of Completeness --- p.84 / Chapter 4.1 --- Theorem of Completeness --- p.84 / Chapter 4.2 --- Construction of Formal Power Series of h and g --- p.86 / Chapter 4.3 --- Proof of Convergence --- p.93

Thesis (Ph. D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 50-53).

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Mathematics." Includes bibliographical references (p. 72-74).

Thesis (Ph.D.)--University of Hong Kong, 2000. / Includes bibliographical references (leaves 50-53) Also available in print.

Thesis (M. Phil.)--University of Hong Kong, 2002. / Includes bibliographical references (leaves 115-118).

published_or_final_version / Mathematics / Master / Master of Philosophy

Orientador: Jorge Tulio Mujica Ascui / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T23:05:35Z (GMT). No. of bitstreams: 1 Bertoloto_FabioJose_D.pdf: 716013 bytes, checksum: 13487be60bd9cd099898dc66a1234a32 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho, estudamos os já conhecidos espaços de Hardy de funções holomorfas Hp(Delta; F), 1 = p = 8. Estudamos também os espaços de Banach com as propriedades RNP e ARNP e os espaços UMD. Tendo introduzido estes, a partir de resultados voltados para o caso complexo dos artigos de Taylor [36], [37], que demonstram que (Hp(Delta ))' e Hq(Delta ) são canonicamente topologicamente isomorfos para 1 < p < 8, com q conjugado de p, demonstramos que sob as condições de F e F' terem a propridade ARNP, (Hp(Delta ; F))' e Hq(Delta ; F') são canonicamente topologicamente isomorfos (para 1 < p, q < 8, 1/p + 1 /q = 1) se, e somente se, F é UMD / Abstract: In this work we study the vector-valued Hardy spaces Hp(Delta ; F) (1 = p = 8). We also study the Banach spaces with the properties ARNP and RNP and the UMD spaces. We also study the Banach spaces with the RNP and ARNP properties, and also the UMD spaces. By following the approach of Taylor [36],[37] in the scalar-valued case, we prove that, when F and F' have the ARNP property, when (Hp(Delta ; F))' and Hq(Delta ; F) are canonically topologically isomorphic (for 1 < p, q < 8, 1/ p + 1/ q = 1) if and only if F is UMD / Doutorado / Analise Funcional / Doutor em Matemática