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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Scaled-oscillation and regularity


Authors: Zoltán M. Balogh and Marianna Csörnyei
Journal: Proc. Amer. Math. Soc. 134 (2006), 2667-2675
MSC (2000): Primary 26B35; Secondary 26B05
Published electronically: March 23, 2006
MathSciNet review: 2213746
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Abstract: We give sufficient conditions for Sobolev and Lipschitz functions in terms of their lower scaled-oscillation. The sharpness of these conditions is shown by examples. Our examples also show that a Stepanov-type differentiability theorem does not hold under the boundedness assumption of the lower scaled-oscillation.


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Additional Information

Zoltán M. Balogh
Affiliation: Mathematisches Institut, Universität Bern, CH–3012 Sidlerstrasse 5, Bern, Switzerland
Email: zoltan.balogh@math-stat.unibe.ch

Marianna Csörnyei
Affiliation: Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
Email: mari@math.ucl.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08290-6
PII: S 0002-9939(06)08290-6
Received by editor(s): May 27, 2004
Received by editor(s) in revised form: April 3, 2005
Published electronically: March 23, 2006
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society