The commutants of certain Toeplitz operators on weighted Bergman spaces

For α > −1, let A2 α be the corresponding weighted Bergman space of the unit ball in Cn. For a bounded measurable function f , let T f be the Toeplitz operator with symbol f on A2 α. This paper describes all the functions f for which T f commutes with a given T g, where g(z) = zL1 1 ··· zLn n for strictly positive integers L1, . . . , Ln, or g(z) = |z1|s1 ···|zn|snh(|z|) for non-negative real numbers s1, . . . , sn and a bounded measurable function h on [0, 1).