Commutators and Semi-commutators of Monomial Toeplitz Operators on the Pluriharmonic Hardy Space

Abstract

In this paper, the authors completely characterize the finite rank commutator and semi-commutator of two monomial Toeplitz operators on the pluriharmonic Hardy space of the torus or the unit sphere. As a consequence, many non-trivial examples of (semi-)commuting Toeplitz operators on the pluriharmonic Hardy spaces are given.

Keywords

Toeplitz operator / Pluriharmonic Hardy space / Commutator / Semicommutator / Monomial symbol

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