Boundedness for iterated commutators on the mixed norm spaces (Q884329)

The aim of this paper is to study commutators of linear operators in weighted Bergman spaces of holomorphic functions on the unit ball of \(\mathbb C^n\). In particular, the authors study the commutator \(C^n_h=[M_h,\dots, [M_h,[M_h,P],\dots]\) where \(M_h\) is the multiplication operator and \(P\) is a reproducing kernel on the weighted Bergman space. The main result of the paper is that the operator \(C^n_h\) is bounded in the space of weighted \(L^2\) functions if and only if \(h\) belongs to the Bloch space, as introduced by Timoney.