Weighted Estimates for the Berezin Transform and Bergman Projection on   the Unit Ball in $\mathbb{C}^{n}$
  Using modern techniques of dyadic harmonic analysis, we are able to prove sharp estimates for the Bergman projection and Berezin transform and more general operators in weighted Bergman spaces on the unit ball in $\mathbb{C}^n$. The estimates are in terms of the Bekolle-Bonami constant of the weight. 
Rob Rahm, Edgar Tchoundja, Brett D. Wick
math.CA