Multiplication Operators on Weighted Zygmund Spaces of the First Cartan Domain

Abstract

Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that are defined on weighted Zygmund spaces of the first Cartan domain. We obtain some necessary conditions and sufficient conditions for the operators to be bounded and compact.

Keywords

• multiplication operator
• first Cartan domain
• weighted Zygmund space
• boundedness
• compactness