NOGUEIRA, T. K.; http://lattes.cnpq.br/6849264023206990; NOGUEIRA, Tony Kleverson.
Résumé:
This work is divided into three parts. In the first, we study the behavior of constants
that satisfy Hardy–Littlewood inequalities to multilinear forms defined in sequence
spaces. Initially, we present the optimal constants for a particular type, called mixed
Littlewood inequality. Then, for other inequalities, we see what happens
to the constants when we disturb the optimal exponents. In the second part, we
solve definitively a problem raised by Carando, Defant and Sevilla–Peris: given the
Bohnenblust–Hille inequality for complex m-homogeneous polynomials whose monomials
have a number of variables uniformly bounded by a positive integer M, we show
that the optimal constants are uniformly bounded, regardless of the value of m. In
the third part, we study lineability in sequence spaces. We show that certain subsets
of some spaces of invariant sequences contain, except for the null sequence, a closed
subspace of infinite dimension.