TOEPLITZ OPERATORS AND SKEW CARLESON MEASURES FOR WEIGHTED BERGMAN SPACES ON STRONGLY PSEUDOCONVEX DOMAINS

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 beta and integrating against a measure y maps continuously a weighted Bergman space A(alpha 1)(p1) (D) into A(alpha 2)(p2) (D) if and only if mu is a (lambda, gamma)-skew Carleson measure, where lambda = 1 + 1/p(1) - 1/P-2 and gamma = 1/lambda(beta + alpha(1)/p(1) - alpha(2)/P-2). 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.