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<p>In this article, the authors determine the optimal regularity of characteristic functions in Besov-type and Triebel–Lizorkin-type spaces under restrictions on the measure of the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10148_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\delta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>-neighborhoods of the boundary. In particular, the necessary and sufficient conditions for the membership in these spaces of characteristic functions of the snowflake domain and also some spiral type domains are obtained.</p>

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Regularity of Characteristic Functions in Besov-Type and Triebel–Lizorkin-Type Spaces

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月17日

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  • Wen Yuan,
  • Winfried Sickel,
  • Dachun Yang

摘要

In this article, the authors determine the optimal regularity of characteristic functions in Besov-type and Triebel–Lizorkin-type spaces under restrictions on the measure of the \(\delta \) δ -neighborhoods of the boundary. In particular, the necessary and sufficient conditions for the membership in these spaces of characteristic functions of the snowflake domain and also some spiral type domains are obtained.