Mathematische Zeitschrift

, Volume 271, Issue 1–2, pp 399–413 | Cite as

Reverse estimates in growth spaces

  • Evgeny Abakumov
  • Evgueni DoubtsovEmail author


Let H(B d ) denote the space of holomorphic functions on the unit ball B d of \({{\mathbb{C}}^d}\). Given a radial doubling weight w, we construct functions \({f, g\in H(B_1)}\) such that |f| + |g| is comparable to w. Also, we obtain similar results for B d , d ≥ 2, and for circular, strictly convex domains with smooth boundary. As an application, we study weighted composition operators and related integral operators on growth spaces of holomorphic functions.


Growth space Circular domain Composition operator Bloch space 

Mathematics Subject Classification (2000)

MSC 30H99 MSC 32A37 MSC 47B38 MSC 30H30 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Laboratoire d’Analyse et de Mathématiques Appliquées, UMR CNRS 8050Université Paris-EstMarne-la-Vallée Cedex 2France
  2. 2.St. Petersburg Department of V.A. Steklov Mathematical InstituteSt. PetersburgRussia

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