Abstract <p>In this paper, we study a Bergman type integral operator <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7228_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="28" /> </InlineMediaObject> <EquationSource Format="TEX">\(E_{t,r}\)</EquationSource>  </InlineEquation> and observe that it preserves <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7228_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(s\)</EquationSource>  </InlineEquation>-Carleson measure on the real unit ball <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7228_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{B}\)</EquationSource>  </InlineEquation> for some appropriate <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7228_Article_IEq6.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(t\)</EquationSource>  </InlineEquation> and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7228_Article_IEq7.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(r\)</EquationSource>  </InlineEquation>. As a consequence, a characterization of the distance from harmonic Bloch-type functions to harmonic <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11957_2025_7228_Article_IEq8.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="67" /> </InlineMediaObject> <EquationSource Format="TEX">\(F(p,q,s)\)</EquationSource>  </InlineEquation> space is established.</p>

Carleson Measures, Harmonic Bloch-Type and \(\boldsymbol{F(p,q,s)}\) Spaces on the Real Unit Ball

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发表日期：

2025年8月26日

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X. Fu,
M. Gao,
X. Xie

摘要

Abstract

In this paper, we study a Bergman type integral operator \(E_{t,r}\) and observe that it preserves \(s\) -Carleson measure on the real unit ball \(\mathbb{B}\) for some appropriate \(t\) and \(r\) . As a consequence, a characterization of the distance from harmonic Bloch-type functions to harmonic \(F(p,q,s)\) space is established.