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<p>The Bargmann-Radon transform, defined by Colombo, Sabadini, and Sommen, is the projection of the real monogenic Bargmann module onto a suitable submodule of monogenic functions. This paper investigates its <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12220_2025_2056_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathcal {L}}^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="script">L</mi> </mrow> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-boundedness and determines the exact norms of two integral operators that are induced by the Bargmann-Radon kernel. Additionally, the Bargmann-Radon transform is extended to the Segal-Bargmann and Bergman modules of polymonogenic functions. The inversion formulas and various reproducing kernels are explicitly calculated.</p>

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Reproducing Kernels and Radon-Type Transforms of Monogenic Functions

  • 期刊论文

  • 发表日期：

    2025年6月11日

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  • Pan Lian

摘要

The Bargmann-Radon transform, defined by Colombo, Sabadini, and Sommen, is the projection of the real monogenic Bargmann module onto a suitable submodule of monogenic functions. This paper investigates its \({\mathcal {L}}^{p}\) L p -boundedness and determines the exact norms of two integral operators that are induced by the Bargmann-Radon kernel. Additionally, the Bargmann-Radon transform is extended to the Segal-Bargmann and Bergman modules of polymonogenic functions. The inversion formulas and various reproducing kernels are explicitly calculated.