Sarason's conjecture of Toeplitz operators on Fock-Sobolev type spaces (Q1749072)

Summary: In this note, we will solve Sarason's conjecture on the Fock-Sobolev type spaces and give a well solution that if Toeplitz product \(T_u T_{\overline{v}}\), with entire symbols \(u\) and \(v\), is bounded if and only if \(u = e^q\), \(v = C e^{-q}\), where \(q\) is a linear complex polynomial and \(C\) is a nonzero constant.