<p>We prove that the commutators <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1756_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(T_b\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>b</mi> </msub> </math></EquationSource> </InlineEquation> with standard Calderón-Zygmund kernel and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1756_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {S}_b\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mi>b</mi> </msub> </math></EquationSource> </InlineEquation> with variable kernel are bounded on variable exponent Hardy spaces when <i>b</i> belongs to some appropriate subspaces of the space of homogeneous Lipschitz functions of order <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1756_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="67" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha \in (0,1]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Commutators of Singular Integrals in Variable Exponent Hardy Spaces

  • Nguyen Duc Trung,
  • Nguyen Ngoc Trong,
  • Le Xuan Truong,
  • Tan Duc Do

摘要

We prove that the commutators \(T_b\) T b with standard Calderón-Zygmund kernel and \(\mathcal {S}_b\) S b with variable kernel are bounded on variable exponent Hardy spaces when b belongs to some appropriate subspaces of the space of homogeneous Lipschitz functions of order \(\alpha \in (0,1]\) α ( 0 , 1 ] .