Sarason’s Toeplitz product problem on the Fock–Sobolev space

Abstract

The Sarason’s Toeplitz product problem asks when the Toeplitz product operator T u T v , with analytic symbols u and v, is bounded on Hilbert space of analytic functions. In this paper, we deal with this problem on the Fock–Sobolev space and have a complete solution that u = e q , v = Ce −q , where q is a linear complex polynomial and C is a nonzero constant.