Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the summablility of truncated double Fourier series   We estimate the truncated double trigonometric series
$\sum_{n=0}^{N}\sum_{m=0}^{M}a_{mn} {e}^{2\pi \imath \left(m x+n y\right)}$,
$a_{mn} \in\mathbb{C}$, in Lebesgue spaces with mixed norms in terms of the
$p^{th}-q^{th}$ power finite double sums of its coefficients. We obtain these
estimates for all possible values of the exponents involved then we provide
examples of matrices in ${\mathbb{C}}^{M\times N}$ that maximize some of them
up to a constant independent of $M$ and $N$.

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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg