Toeplitz operators and skew Carleson measures for weighted Bergman spaces on strongly pseudoconvex domains

Abstract

In this paper we study properties of Toeplitz operators on weighted Bergman spaces of bounded strongly pseudoconvex domains. We prove that a Toeplitz operator built using a weighted Bergman kernel of weight β and integrating against a measure μ maps continuously a weighted Bergman space Ap1α1(D) into Ap2α2(D) if and only if μ is a (λ,γ)-skew Carleson measure, where λ=1+1p1−1p2 and γ=1λ(β+α1p1−α2p2). This generalizes results obtained by Pau and Zhao on the unit ball, and by Abate, Raissy and Saracco on a smaller class of Toeplitz operators on strongly pseudoconvex domains.