Toeplitz Operators on Fock Spaces Fp(φ)

Given satisfying , 0 < p < a, let be the generalized Fock space of all holomorphic functions f on for which the Fock norm While , is the classical Fock space F (p) . In this paper, for all possible 0 < p,q < a we characterize those positive Borel measures mu on for which the induced Toeplitz operators T (mu) are bounded (or compact) from one generalized Fock spaces to another . With symbols , we obtain Zorborska's criterion for boundedness (or compactness) of Toeplitz operators T (g) on F (p) , our work extends the known results on F (2). Toeplitz operators on p-th Fock space with 0 < p < 1 have not been studied before, even in the simplest case that . Our analysis shows a significant difference between Bergman spaces and Fock spaces.