Some classical inequalities, summability of multilinear operators and strange functions

Detalhes bibliográficos
Ano de defesa: 2016
Autor(a) principal: Araújo, Gustavo da Silva
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Federal da Paraíba
Brasil
Matemática
Programa Associado de Pós-Graduação em Matemática
UFPB
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9310
Resumo: 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.