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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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
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