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arXiv · 1904.00041

Hausdorff-Young type inequalities for vector-valued Dirichlet series

Daniel Carando·Felipe Marceca·Pablo Sevilla-Peris
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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 $\mathcal{H}_{p} (X)$ with the $q$-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 $\mathbb{T}^{\infty}$ or the boolean cube $\{-1,1\}^{\infty}$.

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Daniel Carando, Felipe Marceca, Pablo Sevilla-Peris. 2019-03-29. Hausdorff-Young type inequalities for vector-valued Dirichlet series. https://arxiv.org/abs/1904.00041

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