A note on Hadamard–Bergman convolution operators

This paper is a continuation of the recent studies of the class of Hadamard–Bergman operators. The notion of an operator constructed according to the Carleson measure on the Bergman space is introduced, the Berezin transform of the Hadamard–Bergman operator is studied, and the sufficient conditions are given for compactness and belonging to the Schatten ideals in various cases, that is, when the kernel of the operator is a holomorphic function, an L 1 ( D ) function, or when the operator is constructed via the measure of Carleson.