Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Measuring Triebel-Lizorkin fractional smoothness on domains in terms of
  first-order differences   In this note we give equivalent characterizations for a fractional
Triebel-Lizorkin space $F^s_{p,q}(\Omega)$ in terms of first-order differences
in a uniform domain $\Omega$. The characterization is valid for any positive,
non-integer real smoothness $s\in \mathbb{R}_+\setminus \mathbb{N}$ and
{indices $1\leq p<\infty$, $1\leq q \leq \infty$} as long as the fractional
part $\{s\}$ is greater than $d/p-d/q$.

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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex