Commuting Toeplitz and small Hankel operators on the Bergman space

This paper shows that on the Bergman space of the open unit disk, the Toeplitz operator \(T_{{\overline{p}}+\varphi }\) $T_{\overline{p}+\phi }$ and the small Hankel operator \(\Gamma _\psi\) ${\mathrm{\Gamma }}_{\psi }$ commute only in the obvious cases, where \(\varphi\) $\phi$ and \(\psi\) $\psi$ are both bounded analytic functions, and p is an analytic polynomial.