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Bergman Projection in Clifford Analysis

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Clifford Algebras

Part of the book series: Progress in Mathematical Physics ((PMP,volume 34))

Abstract

We study weighted Bergman projections in the monogenic Bergman spaces of the real unit ball \mathbb{B} in ℝ n . We extend results of Forelli—Rudin, Coifman—Rochberg, and Djrbashian to Clifford analysis. The main result is as follows: Let P α be the orthogonal projection from the Hilbert space L 2( \mathbb{B} , Cl 0,n , dV α) onto the subspace of monogenic functions A 2( \mathbb{B} , Cl 0,n , dV α. If p(α + 1) > β + 1 with 1 ≤ p < ∞ and α,β > - 1, then the operator P α : L p ( \mathbb{B} ,Cl 0, n , dV β) → A p( \mathbb{B} ,Cl 0,n , dV β is bounded.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China

    Guangbin Ren

  2. Departamento de Matemática, Universidade de Aveiro, P-3810-193, Aveiro, Portugal

    Helmuth R. Malonek

Authors
  1. Guangbin Ren
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  2. Helmuth R. Malonek
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Tennessee Technological University, 5054, TN 38505, Cookeville, USA

    Rafał Abłamowicz

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© 2004 Birkhäuser Boston

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Ren, G., Malonek, H.R. (2004). Bergman Projection in Clifford Analysis. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_8

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  • DOI: https://doi.org/10.1007/978-1-4612-2044-2_8

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3525-1

  • Online ISBN: 978-1-4612-2044-2

  • eBook Packages: Springer Book Archive

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