Bergman Projection in Clifford Analysis

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 L2( \mathbb{B} , Cl_0,n , dV_α) onto the subspace of monogenic functions A2( \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 : Lp ( \mathbb{B} ,Cl_{0, n} , dV_β) → Ap( \mathbb{B} ,Cl_0,n , dV_β is bounded.