On Toeplitz Operators with Biharmonic Symbols

In this article, we study the commuting problem of Toeplitz operators acting on the Bergman space of the unit disk when one of the symbols is biharmonic. Particularly, we prove that if a Toeplitz operator with right-terminating bounded symbol commutes with a biharmonic symbol, of special form, then it must be a linear combination of the latter one and the constant function.