Some polynomial versions of cotype and applications

DANIEL CARANDO; ANDREAS DEFANT; PABLO SEVILLA PERIS

JOURNAL OF FUNCTIONAL ANALYSIS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2016 vol. 270 p. 68 - 87

0022-1236

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.