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Continuity of the maximal operator in Sobolev spaces
Author(s):
Hannes
Luiro
Journal:
Proc. Amer. Math. Soc.
135
(2007),
243-251.
MSC (2000):
Primary 42B25, 46E35, 47H99
Posted:
June 30, 2006
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Additional information
Abstract:
We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces  ,  . As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.
References:
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Additional Information:
Hannes
Luiro
Affiliation:
Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014 University of Jyväskylä, Finland
Email:
haluiro@maths.jyu.fi
DOI:
10.1090/S0002-9939-06-08455-3
PII:
S 0002-9939(06)08455-3
Keywords:
Maximal function,
Sobolev spaces,
continuity,
regularity
Received by editor(s):
June 4, 2004
Received by editor(s) in revised form:
August 8, 2005
Posted:
June 30, 2006
Additional Notes:
The author was supported by the Academy of Finland, project 201015
Communicated by:
Juha M. Heinonen
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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