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<p>Weighted Bergman projection operators on the Clifford monogenic Bergman spaces over the real ball of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="6_2025_1401_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> have been already studied in a paper of Ren and Malonek. We extend and generalize their results by considering more general Bergman nonprojection operators and stating a necessary and sufficient condition for them to be bounded on weighted Lebesgue spaces. Sharp estimates for the weighted monogenic Bergman kernel are also given.</p>

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Bergman Operators on Clifford Monogenic Bergman Spaces

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Karen Avetisyan,
  • Klaus Gürlebeck

摘要

Weighted Bergman projection operators on the Clifford monogenic Bergman spaces over the real ball of \({\mathbb R}^n\) R n have been already studied in a paper of Ren and Malonek. We extend and generalize their results by considering more general Bergman nonprojection operators and stating a necessary and sufficient condition for them to be bounded on weighted Lebesgue spaces. Sharp estimates for the weighted monogenic Bergman kernel are also given.