# Sums of weighted differentiation composition operators from weighted Bergman spaces to weighted Zygmund and Bloch-type spaces

Jasbir S. Manhas*, Mohammed S. Al Ghafri

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

## Abstract

Let H(D) be the space of analytic functions on the unit disc D and let S(D) denote the set of all analytic self maps of the unit disc D. Let Ψ=(ψj)j=0k be such that ψj∈ H(D) and φ∈ S(D). To treat the Stević–Sharma type operators and the products of composition operators, multiplication operators, differentiation operators in a unified manner, Wang et al. considered the following sum operator: TΨ,φkf=∑j=0kψj·f(j)∘φ=∑j=0kDψj,φjf,f∈H(D).We characterize the boundedness and compactness of the operators TΨ,φk from the weighted Bergman spaces Av,p to the weighted Zygmund-type spaces Zw and the weighted Bloch-type spaces Bw. Besides, giving examples of bounded, unbounded, compact and non-compact operators TΨ,φk, we give an example of two unbounded weighted differentiation composition operators Dψ0,φ0,Dψ1,φ1:Av,p⟶Zw(Bw) such that their sum operator Dψ0,φ0+Dψ1,φ1=TΨ,φ1:Av,p⟶Zw(Bw) is bounded.

Original language English 51 Advances in Operator Theory 6 3 https://doi.org/10.1007/s43036-021-00147-0 Published - Jul 2021 Yes

## Keywords

• Bounded and compact operators
• Weighted Bergman spaces
• Weighted Bloch spaces
• Weighted composition operators
• Weighted differentiation composition operators
• Weighted Zygmund spaces

## ASJC Scopus subject areas

• Analysis
• Algebra and Number Theory