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Inner Mappings, Hyperbolic Gradients and Composition Operators

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Abstract

Let φ be a holomorphic mapping between complex unit balls. We obtain quantitative versions of the following heuristic principle: if the hyperbolic gradient of φ does not grow sufficiently rapidly, then φ is far from being inner.

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Authors and Affiliations

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

    Evgueni Doubtsov

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  1. Evgueni Doubtsov
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Correspondence to Evgueni Doubtsov.

Additional information

This research was supported by RFBR (Grant No. 11-01-00526-a).

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Doubtsov, E. Inner Mappings, Hyperbolic Gradients and Composition Operators. Integr. Equ. Oper. Theory 73, 537–551 (2012). https://doi.org/10.1007/s00020-012-1981-9

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  • DOI: https://doi.org/10.1007/s00020-012-1981-9

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