Volterra operators between limits of Bergman-type weighted spaces of analytic functions

Year 2021, , 949 - 962, 06.08.2021

Ersin Kızgut

https://doi.org/10.15672/hujms.777911

Cited By: 1

Abstract

We characterize continuity and compactness of the Volterra integral operator $T_g$ with the non-constant analytic symbol $g$ between certain weighted Fréchet or (LB)-spaces of analytic functions on the open unit disc, which arise as projective (resp. inductive) limits of intersections (resp. unions) of Bergman spaces of order $1<p<\infty$ induced by the standard radial weight $(1-|z|^2)^\alpha$ for $0<\alpha<\infty$. Motivated from the earlier results obtained for weighted Bergman spaces of standard weight, we also establish several results concerning the spectrum of the Volterra operators acting on the weighted Bergman Fréchet space $A^p_{\alpha+}$, and acting on the weighted Bergman (LB)-space $A^p_{\alpha-}$.

Keywords

Volterra operator, weighted spaces of analytic functions, Bergman spaces, Fréchet spaces, (LB)-spaces, spectrum

Supporting Institution

TÜBİTAK

Project Number

1059B191800828

Thanks

This article was completed during the autor's stay at Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, funded by The Scientific and Technological Research Council of Turkey (TÜBİTAK) with grant number 1059B191800828. The author is deeply thankful to Prof. José Bonet, Prof. Enrique Jordá, and Prof. David Jornet for useful suggestions and kind hospitality.

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