Bergman projection induced by radial weight

Abstract

Contents 24 5. Bergman projection P ω : L p ω Ñ L p ω 27 6. Bergman projection P ω : L p ν Ñ L p ν 33 7. Dual of A 1 ω when ω P p D 39 8. Further comments and open problems 45 8.1. Littlewood-Paley estimates 45 8.2. Boundedness of the Bergman projection 46 References 48

Bergman projections induced by doubling weights on the unit ball of Cn

“…See [9,10] and the references therein for more details about I, R, D. Let D = D ∩ Ď. More information about Ď and D can be found in [7,14].…”

“…The result was extended in [17] for some ω ∈ R. In [13], for ω ∈ R, the Bergman projections P ω and the maximal Bergman projection P + ω on some analytic function spaces on D were studied. In [14], Peláez and Rättyä studied the Bergman projection induced by radial weight on some analytic function spaces on D. They showed that [13,14], in this paper we investigate the boundedness of P ω : L ∞ (B, dV) → B(B) and P ω (P + ω ) : L p (B, υdV) → L p (B, υdV) on the unit ball of C n with p > 1 and ω, υ ∈ D.…”

Toeplitz operators on Bergman spaces induced by doubling weights on the unit ball of $\mathbb{C}^n$

“…By Lemma 1.1 in [15], K ω = 1 if ω is continuous and regular. More information about Ď and D can be seen in [8,19].…”