Toeplitz Operators on the Dirichlet Space of 𝔹 n

Abstract

We study the algebraic properties of Toeplitz operators on the Dirichlet space of the unit ball ${𝔹}_n$. We characterize pluriharmonic symbol for which the corresponding Toeplitz operator is normal or isometric. We also obtain descriptions of conjugate holomorphic symbols of commuting Toeplitz operators. Finally, the commuting problem of Toeplitz operators whose symbols are of the form $z^p{\overline{z}}^q\varphi ({|z|}^2)$ is studied.