Espaços de Hardy e compacidade compensada

• Ano de defesa: 2014
• Autor(a) principal: Souza, Osmar do Nascimento
• Orientador(a): Hoepfner, Gustavo
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• País: BR
• Palavras-chave em Português: Análise harmônica; Hardy, Espaços de; Compacidade compensada; Caracterizaçao maximal de Hp; Decomposiçõo atômica de Hp
• Palavras-chave em Inglês: Harmonic analysis; Hardy spaces Hp; Maximal caracterization of Hp; Atomic decomposition for Hp; Compensated compactness
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/5906

This work is divided into two parts. In the first part, our goal is to present the theory of Hardy Spaces Hp(Rn), which coincides with the Lebesgue space Lp(Rn) for p > 1, is strictly contained in Lp(Rn) if p = 1, and is a space of distributions when 0 < p < 1. When 0 < p ^ 1, the Hardy spaces offers a better treatment involving harmonic analysis than the Lp spaces. Among other results, we prove the maximal characterization theorem of Hp, which gives equivalent definitions of Hp, based on different maximal functions. We will proof the atomic decom¬position theorem for Hp, which allow decompose any distribution in Hp to be written as a sum of Hp-atoms (measurable functions that satisfy certain properties). In this step, we use the strongly the of Whitney decomposition and generalized Calderon-Zygmund decomposition. In the second part, as a application, we will prove that nonlinear quantities (such as the Jacobian, divergent and rotational defined in Rn) identied by the compensated compactness theory belong, under natural conditions, the Hardy spaces. To this end, in addition to the results seen in the first part, will use the results as Sobolev immersions theorems ans the inequality Sobolev-Poincare. Furthermore, we will use the tings and results related to the context of differential forms.