  Sarason Toeplitz product problem asks when the operator TuTv is bounded on
various Hilbert spaces of analytic functions, where u and v are analytic. The
problem is highly nontrivial for Toeplitz operators on the Hardy space and the
Bergman space (even in the case of the unit disk). In this paper, we provide a
complete solution to the problem for a class of Fock spaces on the complex
plane. In particular, this generalizes an earlier result of Cho, Park, and Zhu.
