<p>Let <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> be a finite positive measure on an irreducible bounded symmetric domain <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation> in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb {C}^n$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation>. Let <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq4.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$T_\mu ^\beta $</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>T</mi> <mi>μ</mi> <mi>β</mi> </msubsup> </math></EquationSource> </InlineEquation> be the Toeplitz operator induced by <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\mu $</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation> with a sufficiently large weight parameter <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq6.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>. We characterize the bounded Toeplitz operator <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq4.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="23" /> </InlineMediaObject> <EquationSource Format="TEX">$T_\mu ^\beta $</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>T</mi> <mi>μ</mi> <mi>β</mi> </msubsup> </math></EquationSource> </InlineEquation> acting from a Bergman space <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq8.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$A_{\alpha _1}^{p_1}(\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>A</mi> <mrow> <msub> <mi>α</mi> <mn>1</mn> </msub> </mrow> <msub> <mi>p</mi> <mn>1</mn> </msub> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> to another Bergman space <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43037_2025_455_Article_IEq9.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$A_{\alpha _2}^{p_2}(\Omega )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>A</mi> <mrow> <msub> <mi>α</mi> <mn>2</mn> </msub> </mrow> <msub> <mi>p</mi> <mn>2</mn> </msub> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> in terms of skew Carleson measures and Bergman metric balls.</p>

Toeplitz operators between Bergman spaces in bounded symmetric domains

期刊论文
发表日期：

2025年9月10日

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Cheng Yuan

摘要

Let $\mu $ $μ$ be a finite positive measure on an irreducible bounded symmetric domain $\Omega $ $Ω$ in $\mathbb {C}^n$ $C^{n}$ . Let $T_\mu ^\beta $ $T_{μ}^{β}$ be the Toeplitz operator induced by $\mu $ $μ$ with a sufficiently large weight parameter $\beta $ $β$ . We characterize the bounded Toeplitz operator $T_\mu ^\beta $ $T_{μ}^{β}$ acting from a Bergman space $A_{\alpha _1}^{p_1}(\Omega )$ $A_{α_{1}}^{p_{1}} (Ω)$ to another Bergman space $A_{\alpha _2}^{p_2}(\Omega )$ $A_{α_{2}}^{p_{2}} (Ω)$ in terms of skew Carleson measures and Bergman metric balls.