Muckenhoupt type weights and Berezin formulas for Bergman spaces

[摘要] By means of Muckenhoupt type conditions, we characterize the weights omega on C such that the Bergman projection of F-alpha(2,l) = H(C) boolean AND L-2(C, e(-alpha/2 vertical bar z vertical bar 2l))> alpha > 0, l > 1, is bounded on L-p (C, e(-alpha p/2 vertical bar z vertical bar 2l)omega(z)), for 1 < p < infinity. We also obtain explicit representation integral formulas for functions in the weighted Bergman spaces A(p)(omega) = H(C) boolean AND L-p(omega). Finally, we check the validity of the so called Sarason conjecture about the boundedness of products of certain Toeplitz operators on the spaces F-alpha(p,l) = H(C) boolean AND L-p (C, e(-alpha p/2 vertical bar z vertical bar 2l)). (C) 2021 The Author(s). Published by Elsevier Inc.

[发布日期] 2021-12-01

[关键词] Integral representations;Bergman spaces;Fock spaces;Muckenhoupt type weights;Toeplitz operators