Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extensions of the vector-valued Hausdorff-Young inequalities   In this paper we study the vector-valued analogues of several inequalities
for the Fourier transform. In particular, we consider the inequalities of
Hausdorff--Young, Hardy--Littlewood, Paley, Pitt, Bochkarev and Zygmund. The
Pitt inequalities include the Hausdorff--Young and Hardy--Littlewood
inequalities and state that the Fourier transform is bounded from
$L^p(\mathbb{R}^d,|\cdot|^{\beta p})$ into $L^q(\mathbb{R}^d,|\cdot|^{-\gamma
q})$ under certain condition on $p,q,\beta$ and $\gamma$. Vector-valued
analogues are derived under geometric conditions on the underlying Banach space
such as Fourier type and related geometric properties. Similar results are
derived for $\mathbb{T}^d$ and $\mathbb{Z}^d$ by a transference argument. We
prove sharpness of our results by providing elementary examples on
$\ell^p$-spaces. Moreover, connections with Rademacher (co)type are discussed
as well.

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The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph