Abstract:

We characterized commuting dual Toeplitz operators with pluriharmonic symbols on the orthogonal complement of  Dirichlet space in Sobolev space on the unit ball. We also obtained the sufficient and necessary condition, that is, the product of two dual Toeplitz operators with pluriharmonic symbols for a dual Toeplitz operator.

Key words: Sobolev space, Dirichlet space, dual Toeplitz operator, commutativity