Sum of generalized weighted composition operators between weighted spaces of analytic functions

Mohammed Said Al Ghafri, Jasbir Singh Manhas*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Let be the space of analytic functions on the unit disc and let denote the set of analytic self-maps of . Let ψ = (ψj)j=0k be such that ψj and φ . We characterize the boundedness, compactness and completely continuous of the sum of generalized weighted composition operators Tψ,φkf =Ζ j=0kψ j ⋅ f(j) φ =Ζ j=0k ψj,φjf,f , between weighted Banach spaces of analytic functions Hv∞(H v0) and Hw∞(H w0) which unifies the study of products of composition operators, multiplication operators and differentiation operators. As applications, we obtain the boundedness and compactness of the generalized weighted composition operators ψ,φn:Ζ v(Ζv0) →Ζ w(Ζw0), Ζv(Ζv0) → H w∞(H w0) and Hv∞(H v0) →Ζ w(Ζw0), where Ζv(Ζv0) and Ζw(Ζw0) are weighted Bloch-type (little Bloch-type) spaces. Also, new characterizations of the boundedness and compactness of the operators Tψ,φk and ψ,φn are given. Examples of bounded, unbounded, compact and non-compact operators Tψ,φk and ψ,φn are given to explain the role of inducing functions ψj, φ and the weights v, w of the underlying weighted spaces.

Original languageEnglish
JournalAsian-European Journal of Mathematics
DOIs
Publication statusAccepted/In press - 2022

Keywords

  • bounded and compact operators
  • Composition operators
  • generalized weighted composition operators
  • multiplication operators
  • weighted Banach spaces
  • weighted Bloch-type spaces

ASJC Scopus subject areas

  • Mathematics(all)

Cite this