Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on Malliavin smoothness on the L\'evy space   We consider Malliavin calculus based on the It\^o chaos decomposition of
square integrable random variables on the L\'evy space. We show that when a
random variable satisfies a certain measurability condition, its
differentiability and fractional differentiability can be determined by
weighted Lebesgue spaces. The measurability condition is satisfied for all
random variables if the underlying L\'evy process is a compound Poisson process
on a finite time interval.

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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn