Weighted composition operators on weighted Bergman spaces of the unit ball

Waleed Al-Rawashdeh, Sivaram K. Narayan

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose Φ is an analytic self map of B n and φ is analytic on B n. Then a weighted composition operator induced by Φ with weight φ is given by (W φ,ρf) (z) = φ(z)f(Φ(z)) for z in B n and f analytic on B n. Given W φ,Φ: A p α(B n) → A q βj(B n) we characterize boundedness and compactness of W φ,ρ, where 0 p,q < ∞ and -1 < α, β < ∞. We also characterize the Schatten p-class weighted composition operators S p (A 2 α(B n)) for 0 < p < ∞ and -1< α < ∞.

Original languageEnglish
Pages (from-to)161-183
Number of pages23
JournalInternational Journal of Pure and Applied Mathematics
Volume78
Issue number2
StatePublished - 2012

Keywords

  • Bergman spaces
  • Schatten p-class
  • The Berezin transform
  • Toeplitz operators
  • Unit ball of ℂ
  • Weighted composition operators

Fingerprint

Dive into the research topics of 'Weighted composition operators on weighted Bergman spaces of the unit ball'. Together they form a unique fingerprint.

Cite this