In this article, we consider some algebraic properties of Toeplitz operators on weighted pluriharmonic Bergman space on the unit ball. We characterize the commutants of Toeplitz operators whose symbols are certain separately radial functions or holomorphic monomials, and then give a partial answer to the finite-rank product problem of Toeplitz operators.
"Toeplitz operators on weighted pluriharmonic Bergman space." Banach J. Math. Anal. 12 (2) 439 - 455, April 2018. https://doi.org/10.1215/17358787-2017-0055