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Licensed Unlicensed Requires Authentication 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

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 Lp-norm of theWirtinger derivative . As a consequence we obtain a Korn type inequality for vector fields .

Received: 2009-10-05
Revised: 2010-05-24
Accepted: 2010-06-07
Published Online: 2011-05-04
Published in Print: 2011-June

© de Gruyter 2011