On the commutant of multiplication operators with analytic symbols (Q1430436)

The main purpose of the present paper is to determine the commutant of certain multiplication operators acting on a certain Banach space \(\beta\) of analytic functions on a plane domain \(G\). Indeed, under some sufficient conditions, the authors characterize the commutant of \(M_\varphi\) whenever \(\phi\) takes one of the following forms: (1) \(\varphi(z)= z^2+ az+ b\), (2) \(\phi(z)= a_n z^n+ a_{n-1} z^{n-1}+\cdots a_1z+ a_0\), (3) \(\phi(z)= z^3+ az\), (4) \(\varphi(z)= h+ g\), \(h,g\in M(\beta)\cap A(G)\).