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<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1695_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">\((\mathcal {X}, d, \mu )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="script">X</mi> <mo>,</mo> <mi>d</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> be a metric measure space of homogeneous type and let <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1695_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="117" /> </InlineMediaObject> <EquationSource Format="TEX">\(p(\cdot ): \mathcal {X} \rightarrow (0,1]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> <mo>:</mo> <mi mathvariant="script">X</mi> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation> be a variable exponent function satisfying the globally log-Hölder continuous condition. In this paper, we obtain non-tangential and radial maximal function characterizations for local variable Hardy spaces associated to a non-negative self-adjoint operator satisfying Gaussian estimates on a space of homogeneous type, which extend the result of classical local Hardy spaces by T.&#xa0;A. Bui et al (Trans. Amer. Math. Soc. 370:7229-7292, 2018).</p>

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Maximal Function Characterizations for Local Variable Hardy Spaces Associated to Non-negative Self-Adjoint Operators on Spaces of Homogeneous Type

  • 期刊论文

  • 发表日期：

    2025年5月12日

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  • Yao He,
  • Jianquan Liao

摘要

Let \((\mathcal {X}, d, \mu )\) ( X , d , μ ) be a metric measure space of homogeneous type and let \(p(\cdot ): \mathcal {X} \rightarrow (0,1]\) p ( · ) : X → ( 0 , 1 ] be a variable exponent function satisfying the globally log-Hölder continuous condition. In this paper, we obtain non-tangential and radial maximal function characterizations for local variable Hardy spaces associated to a non-negative self-adjoint operator satisfying Gaussian estimates on a space of homogeneous type, which extend the result of classical local Hardy spaces by T. A. Bui et al (Trans. Amer. Math. Soc. 370:7229-7292, 2018).