Some classical inequalities, summability of multilinear operators and strange functions

• Ano de defesa: 2016
• Autor(a) principal: Araújo, Gustavo da Silva
• 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
• Palavras-chave em Português: Desigualdade de Bohnenblust–Hille; Desigualdade de Hardy–Littlewood; Função contínua; Função diferenciável; Fnção mensurável; Lineabilidade; Operadores multilineares somantes; Bohnenblust–Hille Inequality; Continuous function; Differentiable function; Hardy–Littlewood Inequality; Lineability; Measurable function; Summing multilinear operators; CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/tede/9310

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.