Schatten class weighted composition operators on weighted Hilbert Bergman spaces of bounded strongly pseudoconvex domain

Let D be a bounded strongly pseudoconvex domain in Cn, delta(z) = d(z, partial derivative D) the Euclidean distance from the point z to the boundary partial derivative D and H(D) the set of all holomorphic functions on D. For given beta E R, the weighted Hilbert Bergman space on D, denoted by A2(D, beta), consists of all f E H(D) such that [ 1. ]1 11f112,beta = If(z)I2 delta (z)beta dv(z) 2 < +00, D where dv is the Lebesgue measure on D. The aim of the paper is to completely characterize the Schatten class of weighted composition operators on A2(D, beta) when delta(z) satisfies certain integrable condition.