Commuting dual Toeplitz operators with pluriharmonic symbols

In this paper we completely characterize commuting dual Toeplitz operators with bounded pluriharmonic symbols on the Bergman space of the unit ball. We show that for ϕ and ψ pluriharmonic, SϕSψ = Sψϕ on (L2a (Bn)) ⊥ only in the trivial case. Here the trivial case is ϕ or ¯ψ holomorphic.  2004 Elsevier Inc. All rights reserved