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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A quasiregular analogue of a theorem of Hardy and Littlewood


Author: Craig A. Nolder
Journal: Trans. Amer. Math. Soc. 331 (1992), 215-226
MSC: Primary 30C62
DOI: https://doi.org/10.1090/S0002-9947-1992-1036007-3
MathSciNet review: 1036007
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Abstract: Suppose that $ f$ is analytic in the unit disk. A theorem of Hardy and Littlewood relates the Hölder continuity of $ f$ over the unit disk to the growth of the derivative. We prove here a quasiregular analogue of this result in certain domains in $ n$-dimensional space. We replace values of the derivative with a local integral average. In the process we generalize a result on the continuity of quasiconformal mappings due to Nakki and Palka. We also present another proof of the relationship between the growth of the derivative and quasiregular mappings in BMO.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1036007-3
Keywords: Quasiregular mappings, Hölder continuity, growth of the derivative
Article copyright: © Copyright 1992 American Mathematical Society