Continuity of the maximal operator in Sobolev spaces
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- by Hannes Luiro
- Proc. Amer. Math. Soc. 135 (2007), 243-251
- DOI: https://doi.org/10.1090/S0002-9939-06-08455-3
- Published electronically: June 30, 2006
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Abstract:
We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces $W^{1,p}(\mathbb {R}^n)$, $1<p<\infty$. As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.References
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Bibliographic Information
- Hannes Luiro
- Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014 University of Jyväskylä, Finland
- MR Author ID: 803271
- Email: haluiro@maths.jyu.fi
- Received by editor(s): June 4, 2004
- Received by editor(s) in revised form: August 8, 2005
- Published electronically: June 30, 2006
- Additional Notes: The author was supported by the Academy of Finland, project 201015
- Communicated by: Juha M. Heinonen
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 243-251
- MSC (2000): Primary 42B25, 46E35, 47H99
- DOI: https://doi.org/10.1090/S0002-9939-06-08455-3
- MathSciNet review: 2280193