Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence of double Walsh series universal in weighted $L_\mu^1[0,1]^2$
  spaces   In this paper we consider a question on existence of double Walsh series
universal in weighted $L_\mu^1[0,1]^2$ spaces. We construct a weighted function
$\mu(x,y)$ and a series by double Walsh system of the form
$$\sum_{n,k=1}^\infty c_{n,k}W_n(x)W_k(y)\ \ \mbox{with} \ \
\sum_{n,k=1}^\infty \left | c_{n,k} \right|^q <\infty\ \mbox{for all}\ q>2,$$
which is universal in $L_\mu^1[0,1]^2$ concerning subseries with respect to
convergence, in the sense of both spherical and rectangular partial sums.

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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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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: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat