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 languageEnglish
Article number51
JournalAdvances in Operator Theory
Volume6
Issue number3
DOIs
Publication statusPublished - Jul 2021
Externally publishedYes

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

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