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Strong Hardy–Littlewood theorems for analytic functions and mappings of finite distortion

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Abstract.

A formula is pointed out that explains why an analytic function often enjoys the same smoothness properties as its modulus. This is extended to quasiregular mappings and, mutatis mutandis, to mappings of finite distortion.

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Authors and Affiliations

  1. Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, Gran Via 585, E-08007, Barcelona, Spain

    Konstantin M. Dyakonov

  2. Steklov Institute of Mathematics, St. Petersburg Branch (POMI), Fontanka 27, St. Petersburg, 191023, Russia

    Konstantin M. Dyakonov

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  1. Konstantin M. Dyakonov
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Correspondence to Konstantin M. Dyakonov.

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Mathematics Subject Classification (1991): 30C65, 30D50, 30D55

Supported in part by Grant 02-01-00267 from the Russian Foundation for Fundamental Research, DGICYT Grant BFM2002-04072-C02-01, CIRIT Grant 2001-SGR-00172, by the Ramón y Cajal program (Spain) and by the European Community’s Human Potential Program under contract HPRN-CT-2000-00116 (Analysis and Operators).

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Dyakonov, K. Strong Hardy–Littlewood theorems for analytic functions and mappings of finite distortion. Math. Z. 249, 597–611 (2005). https://doi.org/10.1007/s00209-004-0723-3

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  • DOI: https://doi.org/10.1007/s00209-004-0723-3

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