<p>In this paper, we investigate the boundedness of the maximal operator of the dyadic derivative of the dyadic integral from the variable Hardy space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1928_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="34" /> </InlineMediaObject> <EquationSource Format="TEX">$H_{p(\cdot )}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </msub> </math></EquationSource> </InlineEquation> to the variable Lebesgue space <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1928_Article_IEq2.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">$L_{p(\cdot )}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </msub> </math></EquationSource> </InlineEquation> and from the variable Lorentz-Hardy space <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1928_Article_IEq3.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">$H_{p(\cdot ),q}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> <mo>,</mo> <mi>q</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> to the variable Lorentz space <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1928_Article_IEq4.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$L_{p(\cdot ),q}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mrow> <mi>p</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> <mo>,</mo> <mi>q</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>. The proof depends on some new maximal estimates of dyadic derivative.</p>

Boundedness of the Dyadic Derivative In Variable Hardy Spaces

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发表日期：

2025年7月15日

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Weicong Shu,
Hongli Tian

摘要

In this paper, we investigate the boundedness of the maximal operator of the dyadic derivative of the dyadic integral from the variable Hardy space $H_{p(\cdot )}$ $H_{p (\cdot)}$ to the variable Lebesgue space $L_{p(\cdot )}$ $L_{p (\cdot)}$ and from the variable Lorentz-Hardy space $H_{p(\cdot ),q}$ $H_{p (\cdot), q}$ to the variable Lorentz space $L_{p(\cdot ),q}$ $L_{p (\cdot), q}$ . The proof depends on some new maximal estimates of dyadic derivative.