Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bourgain-Brezis-Mironescu-Maz'ya-Shaposhnikova limit formulae for
  fractional Sobolev spaces via interpolation and extrapolation   The real interpolation spaces between $L^{p}({\mathbb{R}}^{n})$ and $\dot
{H}^{t,p}({\mathbb{R}}^{n})$ (resp. $H^{t,p}({\mathbb{R}}^{n})$), $t>0,$ are
characterized in terms of fractional moduli of smoothness, and the underlying
seminorms are shown to be " the correct" fractional generalization of the
classical Gagliardo seminorms. This is confirmed by the fact that, using the
new spaces combined with interpolation and extrapolation methods, we are able
to extend the Bourgain-Brezis-Mironescu-Maz'ya-Shaposhnikova limit formulae, as
well as the Bourgain-Brezis-Mironescu convergence theorem, to fractional
Sobolev spaces. On the other hand, we disprove a conjecture of \cite{Braz}
suggesting fractional convergence results given in terms of classical Gagliardo
seminorms. We also solve a problem proposed in \cite{Braz} concerning sharp
forms of the fractional Sobolev embedding.

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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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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: math-ph
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The categories of this paper are: astro-ph