Product Type Operators Involving Radial Derivative Operator Acting between Some Analytic Function Spaces

Abstract

Let N denote the set of all positive integers and N0=N∪{0}. For m∈N, let Bm={z∈Cm:|z|1} be the open unit ball in the m−dimensional Euclidean space Cm. Let H(Bm) be the space of all analytic functions on Bm. For an analytic self map ξ=(ξ1,ξ2,…,ξm) on Bm and ϕ1,ϕ2,ϕ3∈H(Bm), we have a product type operator Tϕ1,ϕ2,ϕ3,ξ which is basically a combination of three other operators namely composition operator Cξ, multiplication operator Mϕ and radial derivative operator R. We study the boundedness and compactness of this operator mapping from weighted Bergman–Orlicz space AσΨ into weighted type spaces Hω∞ and Hω,0∞.

Keywords

• weighted Bergman–Orlicz spaces
• composition operator
• multiplication operator
• radial derivative
• weighted-type spaces
• little weighted type spaces