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Weighted composition operators on growth spaces

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Abstract

Denote by Hol(B n ) the space of all holomorphic functions in the unit ball B n of ℂn, n ≥ 1. Given g ∈ Hol(B m ) and a holomorphic mapping φ: B m → B n , put C g φ f = g · (f ∘ φ) for f ∈ Hol(B n ). We characterize those g and φ for which C g φ is a bounded (or compact) operator from the growth space A −log(B n ) or A −β(B n ), β > 0, to the weighted Bergman space A p α (B m ), 0 < p < ∞, α > −1. We obtain some generalizations of these results and study related integral operators.

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

    E. S. Dubtsov

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  1. E. S. Dubtsov
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Correspondence to E. S. Dubtsov.

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Original Russian Text Copyright © 2009 Dubtsov E. S.

The author was supported by the Russian Foundation for Basic Research (Grant 08-01-00358-a) and the Russian Science Support Foundation.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 6, pp. 1269–1279, November–December, 2009.

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Dubtsov, E.S. Weighted composition operators on growth spaces. Sib Math J 50, 998–1006 (2009). https://doi.org/10.1007/s11202-009-0110-8

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  • DOI: https://doi.org/10.1007/s11202-009-0110-8

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