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<p>We introduce the weighted hyperharmonic Bergman space of the slice hyperharmonic functions on the quaternionic unit ball with respect to a slice extension of the familiar Laplace operator, extending the weighted harmonic Bergman space on the unit disc of the complex plane. We give the closed form of its reproducing kernel and establish a special Hilbertian decomposition. The main results concern different integral representations for the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>-slice hyperharmonic functions. Mainly, we provide an isometric isomorphism integral transform of Bargmann type for the weighted hyperharmonic Bergman space, with a special configuration space.</p>

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Integral Representations for the Slice Hyperharmonic Bergman Space

  • 期刊论文

  • 发表日期：

    2026年3月12日

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  • Lamya Bouali,
  • Allal Ghanmi

摘要

We introduce the weighted hyperharmonic Bergman space of the slice hyperharmonic functions on the quaternionic unit ball with respect to a slice extension of the familiar Laplace operator, extending the weighted harmonic Bergman space on the unit disc of the complex plane. We give the closed form of its reproducing kernel and establish a special Hilbertian decomposition. The main results concern different integral representations for the \(L^2\) L 2 -slice hyperharmonic functions. Mainly, we provide an isometric isomorphism integral transform of Bargmann type for the weighted hyperharmonic Bergman space, with a special configuration space.