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

Manisha Devi,Kuldip Raj,Mohammad Mursaleen

doi:10.3390/math9192447

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∞.

Highlights

For 0 < p < ∞ and σ > −1, the weighted Bergman space Aσ (Bm ) = Aσ , consists of m all those functions f ∈ H (B ) for which we have the following norm
For ω ≡ 1, the space H ∞ get reduced to the the space H ∞ of weighted-type spaces Hσ,0 ω bounded analytic function on Bergman space Aσ (Bm)
The weighted-type spaces have been studied by various authors see e.g., [4,5,6] and the references therein

Summary

Introduction

For 0 < p < ∞ and σ > −1, the weighted Bergman space Aσ (Bm ) = Aσ , consists of m all those functions f ∈ H (B ) for which we have the following norm For ω ≡ 1, the space H ∞ get reduced to the the space H ∞ of weighted-type spaces Hσ,0 ω bounded analytic function on Bm . The weighted-type spaces have been studied by various authors see e.g., [4,5,6] and the references therein. More results on weighted composition operators on class of holomorphic functions can be found in [7,8] and the references therein.

Objectives

Results

Conclusion