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<p>This paper considers Morrey spaces and Sobolev–Morrey spaces on the <i>n</i>-dimensional Euclidean space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10998_2025_665_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. An equivalence theorem is proved for the <i>K</i>-functional and the moduli of continuity for these spaces. As an application, we characterize Nikol’skii–Besov–Morrey spaces and hence Triebel–Lizorkin–Morrey spaces via the real interpolation.</p>

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An equivalence theorem for K-functional and moduli of continuity on Morrey spaces and some of its applications

  • 期刊论文

  • 发表日期：

    2025年7月20日

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  • Arash Ghorbanalizadeh,
  • Tahereh Khazaee,
  • Yoshihiro Sawano

摘要

This paper considers Morrey spaces and Sobolev–Morrey spaces on the n-dimensional Euclidean space \(\mathbb {R}^n\) R n . An equivalence theorem is proved for the K-functional and the moduli of continuity for these spaces. As an application, we characterize Nikol’skii–Besov–Morrey spaces and hence Triebel–Lizorkin–Morrey spaces via the real interpolation.