<p>We characterize the Schatten class Toeplitz operators associated with a positive Borel measure on the weighted harmonic Bergman space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_448_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">$L_{h,\omega }^2(\mathbb {D})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>h</mi> <mo>,</mo> <mi>ω</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">D</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> over the unit disk. Furthermore, we establish the necessary and sufficient condition for the Toeplitz operators on <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_448_Article_IEq1.gif" Format="GIF" Height="23" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">$L_{h,\omega }^2(\mathbb {D})$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mrow> <mi>h</mi> <mo>,</mo> <mi>ω</mi> </mrow> <mn>2</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">D</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> belonging to the Schatten <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_448_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\hbar$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ħ</mi> </math></EquationSource> </InlineEquation>-class, where <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43034_2025_448_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\hbar$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ħ</mi> </math></EquationSource> </InlineEquation> is defined as a continuous increasing convex function.</p>

Schatten class Toeplitz operators on weighted harmonic Bergman spaces induced by doubling weights

期刊论文
发表日期：

2025年7月5日

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Min Dong,
Yongjiang Duan,
Sawlet Junis

摘要

We characterize the Schatten class Toeplitz operators associated with a positive Borel measure on the weighted harmonic Bergman space $L_{h,\omega }^2(\mathbb {D})$ $L_{h, ω}^{2} (D)$ over the unit disk. Furthermore, we establish the necessary and sufficient condition for the Toeplitz operators on $L_{h,\omega }^2(\mathbb {D})$ $L_{h, ω}^{2} (D)$ belonging to the Schatten $\hbar$ $ħ$ -class, where $\hbar$ $ħ$ is defined as a continuous increasing convex function.