An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions

Martin Fuchs

doi:10.1515/jaa.2011.008

Published by De Gruyter May 4, 2011

An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions

Martin Fuchs

From the journal Journal of Applied Analysis

https://doi.org/10.1515/jaa.2011.008

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Abstract

Let ƒ : B → ℂ denote a Sobolev function of class defined on the unit disc. We show that the distance of ƒ to the class of all holomorphic functions measured in the norm of the space is bounded by the L^p-norm of theWirtinger derivative . As a consequence we obtain a Korn type inequality for vector fields .

Keywords.: Sobolev spaces; holomorphic functions; Korn type inequalities

Received: 2009-10-05

Revised: 2010-05-24

Accepted: 2010-06-07

Published Online: 2011-05-04

Published in Print: 2011-June

An estimate for the distance of a complex valued Sobolev function defined on the unit disc to the class of holomorphic functions

Abstract

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