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 .
Banach J. Math. Anal.
12(2):
456-480
(April 2018).
DOI: 10.1215/17358787-2017-0035