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<p>In this paper, we introduce the weighted anisotropic local Hardy spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_77_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\(h_{w, N}^p(\mathbb{R}^n ; A)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>h</mi> <mrow> <mi>w</mi> <mo>,</mo> <mi>N</mi> </mrow> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo>;</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_77_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="66" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\in(0,1] \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation>, via the local non-tangential grand maximal function. We alsoestablish the atomic decompositions for the weighted anisotropic local Hardy spaces <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_77_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\(h_{w, N}^p(\mathbb{R}^n ; A)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>h</mi> <mrow> <mi>w</mi> <mo>,</mo> <mi>N</mi> </mrow> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo>;</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>. In addition, we obtain the duality between <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_77_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">\(h_{w, N}^p(\mathbb{R}^n ; A)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>h</mi> <mrow> <mi>w</mi> <mo>,</mo> <mi>N</mi> </mrow> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> <mo>;</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and the weighted anisotropic Campanato type spaces.</p>

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Weighted anisotropic local Hardy spaces

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Y. He

摘要

In this paper, we introduce the weighted anisotropic local Hardy spaces \(h_{w, N}^p(\mathbb{R}^n ; A)\) h w , N p ( R n ; A ) with \(p\in(0,1] \) p ∈ ( 0 , 1 ] , via the local non-tangential grand maximal function. We alsoestablish the atomic decompositions for the weighted anisotropic local Hardy spaces \(h_{w, N}^p(\mathbb{R}^n ; A)\) h w , N p ( R n ; A ) . In addition, we obtain the duality between \(h_{w, N}^p(\mathbb{R}^n ; A)\) h w , N p ( R n ; A ) and the weighted anisotropic Campanato type spaces.