<p>A family of <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-Bergman–Morrey spaces <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$A^{p,\lambda ,\alpha }$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>α</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> in the unit disk <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\mathbb {D}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">D</mi> </math></EquationSource> </InlineEquation> is introduced. Some basic properties of <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$A^{p,\lambda ,\alpha }$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>α</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> are obtained. Subsequently, a Banach algebra structure is given to the <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-Bergman–Morrey spaces <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq9.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$A^{p, \lambda ,\alpha }$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>α</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> via the Duhamel product. In addition, the boundedness, compactness, norm, and essential norm of Volterra integral operators <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq10.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$T_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>T</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq11.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$S_g$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>g</mi> </msub> </math></EquationSource> </InlineEquation> acting on <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>-Bergman–Morrey spaces <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="9_2025_2959_Article_IEq5.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">$A^{p,\lambda ,\alpha }$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>A</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>λ</mi> <mo>,</mo> <mi>α</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> are investigated comprehensively.</p>

$\alpha $-Bergman–Morrey Spaces and Volterra Integral Operators

期刊论文
发表日期：

2025年9月26日

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Xiangling Zhu,
Rong Yang

摘要

A family of $\alpha $ $α$ -Bergman–Morrey spaces $A^{p,\lambda ,\alpha }$ $A^{p, λ, α}$ in the unit disk $\mathbb {D}$ $D$ is introduced. Some basic properties of $A^{p,\lambda ,\alpha }$ $A^{p, λ, α}$ are obtained. Subsequently, a Banach algebra structure is given to the $\alpha $ $α$ -Bergman–Morrey spaces $A^{p, \lambda ,\alpha }$ $A^{p, λ, α}$ via the Duhamel product. In addition, the boundedness, compactness, norm, and essential norm of Volterra integral operators $T_g$ $T_{g}$ and $S_g$ $S_{g}$ acting on $\alpha $ $α$ -Bergman–Morrey spaces $A^{p,\lambda ,\alpha }$ $A^{p, λ, α}$ are investigated comprehensively.

\(\alpha \)-Bergman–Morrey Spaces and Volterra Integral Operators

摘要