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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On a class of quasiconformal functions in Banach spaces

Author: Su Shing Chen
Journal: Proc. Amer. Math. Soc. 37 (1973), 545-548
MSC: Primary 32H15; Secondary 32K05
MathSciNet review: 0318518
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Abstract: A quasiconformal function f on a domain D in a complex Banach space E is defined as a function on D such that for every holomorphic mapping $ \Phi $ from the unit disk $ \Delta $ into D the composite mapping $ f \circ \Phi $ is quasiconformal in the usual sense. With respect to the Kobayashi-Kiernan pseudo distance on D, Schwarz's lemma, Liouville's theorem and the little Picard theorem are obtained for quasiconformal functions. A maximum modulus principle is also obtained for quasiconformal functions.

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Keywords: Quasiconformal function, Kobayashi pseudo distance, Schwarz lemma, Liouville theorem, the little Picard theorem, maximum modulus principle
Article copyright: © Copyright 1973 American Mathematical Society