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Reverse estimates in growth spaces

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Abstract

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.

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Authors and Affiliations

  1. Laboratoire d’Analyse et de Mathématiques Appliquées, UMR CNRS 8050, Université Paris-Est, 5 Boulevard Descartes, Champs-sur-Marne, 77454, Marne-la-Vallée Cedex 2, France

    Evgeny Abakumov

  2. St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia

    Evgueni Doubtsov

Authors
  1. Evgeny Abakumov
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  2. Evgueni Doubtsov
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Correspondence to Evgueni Doubtsov.

Additional information

E. Abakumov was partially supported by the ANR project DYNOP; E. Doubtsov was partially supported by RFBR.

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Abakumov, E., Doubtsov, E. Reverse estimates in growth spaces. Math. Z. 271, 399–413 (2012). https://doi.org/10.1007/s00209-011-0869-8

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  • DOI: https://doi.org/10.1007/s00209-011-0869-8

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