<p>In this paper, we study Hausdorff operator <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1832_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {H}_\mu $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">H</mi> <mi>μ</mi> </msub> </math></EquationSource> </InlineEquation> on weighted mixed norm Fock spaces <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1832_Article_IEq2.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$F_\phi ^{p,q}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mi>ϕ</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </msubsup> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1832_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="99" /> </InlineMediaObject> <EquationSource Format="TEX">$1\le p,q\le \infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo>≤</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. The boundedness and compactness of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1832_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {H}_\mu $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">H</mi> <mi>μ</mi> </msub> </math></EquationSource> </InlineEquation> on <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1832_Article_IEq5.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$F_\phi ^{p,q}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mi>ϕ</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </msubsup> </math></EquationSource> </InlineEquation> are characterized, and we give when <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1832_Article_IEq6.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathcal {H}_\mu $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">H</mi> <mi>μ</mi> </msub> </math></EquationSource> </InlineEquation> on <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1832_Article_IEq7.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="31" /> </InlineMediaObject> <EquationSource Format="TEX">$F_\phi ^{p,q}$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>F</mi> <mi>ϕ</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </msubsup> </math></EquationSource> </InlineEquation> is power bounded or uniformly mean ergodic.</p>

Hausdorff Operators on Weighted Mixed Norm Fock Spaces

期刊论文
发表日期：

2025年2月6日

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Yongqing Liu

摘要

In this paper, we study Hausdorff operator $\mathcal {H}_\mu $ $H_{μ}$ on weighted mixed norm Fock spaces $F_\phi ^{p,q}$ $F_{ϕ}^{p, q}$ for $1\le p,q\le \infty $ $1 \leq p, q \leq \infty$ . The boundedness and compactness of $\mathcal {H}_\mu $ $H_{μ}$ on $F_\phi ^{p,q}$ $F_{ϕ}^{p, q}$ are characterized, and we give when $\mathcal {H}_\mu $ $H_{μ}$ on $F_\phi ^{p,q}$ $F_{ϕ}^{p, q}$ is power bounded or uniformly mean ergodic.