Generalização do conceito de lineabilidade e abordagem multipolinomial de desigualdades clássicas

Abstract

In this work we investigate lineability results and multipolynomial variants of classical inequalities. In the rst part, inspired by a paper published by I. J. Maddox, in 1987, we prove a lineability result related to absolutely summing operators in sequence spaces. Next, we introduce a more restrictive notion of lineability and generalize theorems on the lineability of the sets `p S 0<q<p `q and Lp[0; 1] S q>p Lq[0; 1]. Moreover, this new approach is also explored in the context of Peano curves, motivated by a paper due to Albuquerque et al., 2014. In the second part, we present a brief study on homogeneous multipolynomials, with the aim to obtain multipolynomial variants of the Kahane{Salem{Zygmund and Hardy{Littlewood inequalities.