Extended Ces$\acute{a}$RO Operators on Zygmund Spaces in the Unit Ball

Abstract

Let $g$ be a holomorphic function of the unit ball $B$ in the $n$-dimensional space, and denote by $T_g$ and $I_g$ the induced extended Ces$\acute{a}$ro operator and another integral operator. The boundedness and compactness of $T_g$ and $I_g$ acting on the Zygmund spaces in the unit ball are discussed and necessary and sufficient conditions are given in this paper.