Fock spaces and relative operators

Abstract

This paper is a timely survey on generalized Fock spaces and operators acting on them. It contains the definition of Fock spaces with various weights, the precise estimates on the Bergman kernel, the equivalent norms and the Carleson measures. Also, some recent progress on the study of certain operators on Fock spaces is introduced, which includes composition operators, extended Cesaro operators, Toeplitz operators, Hankel operators, and those in the closed algebra generated by weakly localized operators.