Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A bound for Mean values of Fourier transforms   We show that there exists a sequence $\{n_k, k\ge 1\}$ growing at least
geometrically such that for any finite non-negative measure $\nu$ such that
$\hat \nu\ge 0$, any $T>0$, $$ \int_{-2^{n_k} T}^{2^{n_k} T} \hat \nu(x) \dd x
\ll_\e T\,2^{2^{(1+\e)n_k}} \int_\R \Big|{\sin {xT} \over xT} \Big|^{n_k^2}
\nu(\dd x). $$

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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat