Some polynomial versions of cotype and applications

Abstract

We introduce non-linear versions of the classical cotype of Banach spaces. We show that spaces with l.u.st and cotype, and that spaces having Fourier cotype enjoy our non-linear cotype. We apply these concepts to get results on convergence of vector-valued power series in infinite many variables and on ${\ell }_1$-multipliers of vector-valued Dirichlet series. Finally we introduce cotype with respect to indexing sets, an idea that includes our previous definitions.

References in corpus (1)

• Bohr's absolute convergence problem for ${\mathcal{H}}_p$-Dirichlet series in Banach spaces

Cited by in corpus (1)

• A note on abscissas of Dirichlet series