A major open problem in the theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator, that is, the set of all bounded Toeplitz operators that commute with it. In this paper, we provide a complete description of bounded Toeplitz operators T f , where the symbol f has a truncated polar decomposition, that commute with a Toeplitz operator, whose symbol is the sum of a quasihomogeneous function and a bounded analytic function.
Bouhali et al. (Thu,) studied this question.