Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2013-01-01

Journal: ABSTRACT AND APPLIED ANALYSIS

Included Journals: SCIE

ISSN: 1085-3375

Abstract: We study some algebraic properties of Toeplitz operator with quasihomogeneous or separately quasihomogeneous symbol on the pluriharmonic Bergman space of the unit ball in C-n. We determine when the product of two Toeplitz operators with certain separately quasi-homogeneous symbols is a Toeplitz operator. Next, we discuss the zero-product problem for several Toeplitz operators, one of whose symbols is separately quasihomogeneous and the others are quasi-homogeneous functions, and show that the zero-product problem for two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary. Finally, we also characterize the commutativity of certain quasihomogeneous or separately quasihomogeneous Toeplitz operators.