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Reverse estimates in growth spaces
Authors:Evgeny Abakumov  Evgueni Doubtsov
Institution: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
2. St. Petersburg Department of V.A. Steklov Mathematical Institute, Fontanka 27, 191023, St. Petersburg, Russia
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.
Keywords:
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