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<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_65_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_{\alpha}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>α</mi> </msub> </math></EquationSource> </InlineEquation> be an <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_65_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(m\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>m</mi> </math></EquationSource> </InlineEquation>-linear fractional Calderón–Zygmund operator with kernel of mild regularity, and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_65_Article_IEq3.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="135" /> </InlineMediaObject> <EquationSource Format="TEX">\(\vec{b} =(b_{1},b_{2} ,\ldots,b_{m})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>b</mi> <mo stretchy="false">→</mo> </mover> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>b</mi> <mi>m</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> be a collection of locally integrable functions. In this paper, the main purpose is to establish some estimates for the mapping property of the multilinear commutators <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_65_Article_IEq4.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="38" /> </InlineMediaObject> <EquationSource Format="TEX">\( T_{{\alpha,\Sigma \vec{b}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mrow> <mi>α</mi> <mo>,</mo> <mi mathvariant="normal">Σ</mi> <mover accent="true"> <mi>b</mi> <mo stretchy="false">→</mo> </mover> </mrow> </msub> </math></EquationSource> </InlineEquation> in the context of the variable exponent function spaces. The key tools used are the Fourier series and the pointwise estimates involving the sharp maximal operator of the multilinear commutator and certain associated maximal operators.</p>

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Characterization for boundedness of some commutators of the multilinear fractional Calderón–Zygmund operators with Dini type kernel

  • 期刊论文

  • 发表日期：

    2025年2月21日

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  • W. Zhao,
  • J. Wu

摘要

Let \(T_{\alpha}\) T α be an \(m\) m -linear fractional Calderón–Zygmund operator with kernel of mild regularity, and \(\vec{b} =(b_{1},b_{2} ,\ldots,b_{m})\) b → = ( b 1 , b 2 , … , b m ) be a collection of locally integrable functions. In this paper, the main purpose is to establish some estimates for the mapping property of the multilinear commutators \( T_{{\alpha,\Sigma \vec{b}}}\) T α , Σ b → in the context of the variable exponent function spaces. The key tools used are the Fourier series and the pointwise estimates involving the sharp maximal operator of the multilinear commutator and certain associated maximal operators.