Hausdorff-Young type inequalities for vector-valued Dirichlet series
Abstract
We study Hausdorff-Young type inequalities for vector-valued Dirichlet series which allow to compare the norm of a Dirichlet series in the Hardy space with the -norm of its coefficients. In order to obtain inequalities completely analogous to the scalar case, a Banach space must satisfy the restrictive notion of Fourier type/cotype. We show that variants of these inequalities hold for the much broader range of spaces enjoying type/cotype. We also consider Hausdorff-Young type inequalities for functions defined on the infinite torus or the boolean cube .
Keywords
Cite
@article{arxiv.1904.00041,
title = {Hausdorff-Young type inequalities for vector-valued Dirichlet series},
author = {Daniel Carando and Felipe Marceca and Pablo Sevilla-Peris},
journal= {arXiv preprint arXiv:1904.00041},
year = {2019}
}
Comments
The main contribution of the resubmitted version is that we have been able to show the equivalence between type/cotype and its polynomial counterpart. Therefore, the inequalities for vector-valued Dirichlet series that were obtained in the previous version actually hold assuming only type/cotype