Commutativity of the Berezin Transform of the Pluriharmonic Functions

Let B be the open unit ball in the n-space Cⁿ and T_u be the Toeplitz operator on the Bergman space (B) with symbol u. For u∈L^∞, the Berezin transform of u, is denoted by ũ and is defined as ũ (z) = <T_uk_z, k_z>. In the present paper we discuss the multiplication and commutativity of the Berezin transform of the pluriharmonic functions.