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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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