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Abstract <p> We study how Besov spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(B^s_{p,p}(\mathbb R^2)\)</EquationSource> </InlineEquation> and Bessel potential spaces <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^s_p(\mathbb R^2)\)</EquationSource> </InlineEquation> can be described as intersections of tensor products of the associated univariate spaces with <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L_p(\mathbb R)\)</EquationSource> </InlineEquation>. This generalizes a well-known result by Griebel and Oswald for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H^1(\mathbb R^2)\)</EquationSource> </InlineEquation> in various directions. </p>

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Intersection Representations of Besov and Bessel Potential Spaces Involving Tensor Products

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Markus Hansen,
  • Winfried Sickel,
  • Dachun Yang,
  • Wen Yuan

摘要

Abstract

We study how Besov spaces \(B^s_{p,p}(\mathbb R^2)\) and Bessel potential spaces \(H^s_p(\mathbb R^2)\) can be described as intersections of tensor products of the associated univariate spaces with \(L_p(\mathbb R)\) . This generalizes a well-known result by Griebel and Oswald for \(H^1(\mathbb R^2)\) in various directions.