Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk - Yanyue Shi; Na Zhou (Abstract and Applied Analysis)
We consider the reducing subspaces of MzN on Aα2(Dk), where k≥3, zN=z1N1⋯zkNk, and Ni≠Nj for i≠j. We prove that each reducing subspace of MzN is a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases that α=0 and α∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces of MzN on Aα2(D3) with α>-1.