Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fock-Sobolev spaces of fractional order   For the full range of index $0<p\leq\infty$, real weight $\alpha$ and real
Sobolev order $s$, two types of weighted Fock-Sobolev spaces over $\mathbb
C^n$, $F^p_{\alpha, s}$ and $\widetilde F^p_{\alpha,s}$, are introduced through
fractional differentiation and through fractional integration, respectively. We
show that they are the same with equivalent norms and, furthermore, that they
are identified with the weighted Fock space $F^p_{\alpha-sp,0}$ for the full
range of parameters. So, the study on the weighted Fock-Sobolev spaces is
reduced to that on the weighted Fock spaces. We describe explicitly the
reproducing kernels for the weighted Fock spaces and then establish the
boundedness of integral operators induced by the reproducing kernels. We also
identify dual spaces, obtain complex interpolation result and characterize
Carleson measures.

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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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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: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex