Mellin Transform, Monomial Symbols, and Commuting Toeplitz Operators

In this paper we give necessary and sufficient conditions for a symbol that produces a Toeplitz operator on the Bergman space that commutes with another such operator whose symbol is a monomial. The result is stated in terms of the Mellin transform of the symbol. As a corollary, we show that a Toeplitz operator with a radial symbol may only commute with another such operator with a radial symbol.