Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parabolic Littlewood-Paley inequality for $\phi(-\Delta)$-type operators
  and applications to Stochastic integro-differential equations   In this paper we prove a parabolic version of the Littlewood-Paley inequality
for the operators of the type $\phi(-\Delta)$, where $\phi$ is a Bernstein
function. As an application, we construct an $L_p$-theory for the stochastic
integro-differential equations of the type $du=(-\phi(-\Delta)u+f)dt +gdW_t$.

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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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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: stat
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The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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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: alg-geom
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The categories of this paper are: quant-ph