In this paper, we give a uniform characterization for the reducing subspaces for with the symbol () on the Bergman spaces over the bidisk, including the known cases that and with . Meanwhile, the reducing subspaces for () on the Bergman space over the unit disk are also described. Finally, we state these results in terms of the commutant algebra .
"Reducing subspaces for a class of nonanalytic Toeplitz operators." Banach J. Math. Anal. 12 (2) 456 - 480, April 2018. https://doi.org/10.1215/17358787-2017-0035