Commuting dual Toeplitz operators with pluriharmonic symbols

摘要

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 phi and psi pluriharmonic, SphiSpsi = S-psiphi on (L-2(a)(Bn))(perpendicular to) only in the trivial case. Here the trivial case is phi or psi holomorphic. (C) 2004 Elsevier Inc. All rights reserved.