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Scaled-oscillation and regularity
Author(s):
Zoltán
M.
Balogh;
Marianna
Csörnyei
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2667-2675.
MSC (2000):
Primary 26B35;
Secondary 26B05
Posted:
March 23, 2006
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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:
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
Posted:
March 23, 2006
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2006,
American Mathematical Society
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