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Univalent symbols of Volterra operators on growth spaces

  • Evgeny Abakumov
  • Evgueni DoubtsovEmail author
Article
  • 19 Downloads

Abstract

Let w and v be arbitrary radial weights on the unit disk \({\mathbb {D}}\). We characterize those univalent symbols \(g\in Hol({\mathbb {D}})\) for which the Volterra operator \(T_g\) maps boundedly the growth space \({\mathcal {A}}^w({\mathbb {D}})\) into \({\mathcal {A}}^v({\mathbb {D}})\).

Keywords

Associated weights Growth spaces Univalent functions Volterra operators 

Mathematics Subject Classification

30H99 47B38 

Notes

Compliance with ethical standards

Conflict of interest

No potential conflict of interest was reported by the authors.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.LAMA (UMR 8050)Université Paris-EstMarne-la-ValléeFrance
  2. 2.St. Petersburg Department of V.A. Steklov Institute of MathematicsSt. PetersburgRussia

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