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Analytic functions in Smirnov classes $$E^p$$ with real boundary values II

Analytic functions in Smirnov classes $$E^p$$ with real boundary values II Multiply connected Smirnov domains with non-smooth boundaries may admit non-trivial functions of Smirnov class $$E^p$$ with real boundary values for certain $$p\ge 1$$ . This paper describes the particular geometric boundary characteristics of multiply connected Smirnov domains that make the existence of such functions possible. This extends the similar results in De Castro and Khavinson (2012) obtained for simply connected domains. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Analytic functions in Smirnov classes $$E^p$$ with real boundary values II

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Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer Basel AG
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-012-0036-3
Publisher site
See Article on Publisher Site

Abstract

Multiply connected Smirnov domains with non-smooth boundaries may admit non-trivial functions of Smirnov class $$E^p$$ with real boundary values for certain $$p\ge 1$$ . This paper describes the particular geometric boundary characteristics of multiply connected Smirnov domains that make the existence of such functions possible. This extends the similar results in De Castro and Khavinson (2012) obtained for simply connected domains.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Sep 26, 2012

References