<p>The boundedness and compactness of differences of weighted composition operators from weighted Bergman spaces <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_115_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$A^p_\omega(\mathbb{B}_n)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>A</mi> <mi>ω</mi> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">B</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> induced by a doubling weight <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_115_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> to Lebesgue spaces <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_115_Article_IEq3.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="51" /> </InlineMediaObject> <EquationSource Format="TEX">$L^q_\mu(\mathbb{B}_n)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>L</mi> <mi>μ</mi> <mi>q</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">B</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> are characterized on the unit ball and for the entire range <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_115_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="98" /> </InlineMediaObject> <EquationSource Format="TEX">$0<p,q<\infty$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo><</mo> <mi>p</mi> <mo>,</mo> <mi>q</mi> <mo><</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>, which extend many results in the literatures. As a byproduct, a new characterization of <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_115_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$q$</EquationSource> <EquationSource Format="MATHML"><math> <mi>q</mi> </math></EquationSource> </InlineEquation>-Carleson the measure for <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10476_2025_115_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">$A^p_\omega(\mathbb{B}_n)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi>A</mi> <mi>ω</mi> <mi>p</mi> </msubsup> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="double-struck">B</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> in terms of the Bergman metric ball is also presented.</p>

Difference of weighted composition operators on weighted Bergman spaces over the unit ball

期刊论文
发表日期：

2025年9月10日

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L. Hu,
S. Li,
Y. Shi

摘要

The boundedness and compactness of differences of weighted composition operators from weighted Bergman spaces $A^p_\omega(\mathbb{B}_n)$ $A_{ω}^{p} (B_{n})$ induced by a doubling weight $\omega$ $ω$ to Lebesgue spaces $L^q_\mu(\mathbb{B}_n)$ $L_{μ}^{q} (B_{n})$ are characterized on the unit ball and for the entire range $0<p,q<\infty$ $0 < p, q < \infty$ , which extend many results in the literatures. As a byproduct, a new characterization of $q$ $q$ -Carleson the measure for $A^p_\omega(\mathbb{B}_n)$ $A_{ω}^{p} (B_{n})$ in terms of the Bergman metric ball is also presented.