Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the regularity of maximal operators


Authors: Emanuel Carneiro and Diego Moreira
Journal: Proc. Amer. Math. Soc. 136 (2008), 4395-4404
MSC (2000): Primary 42B25, 54C08, 46E35
Published electronically: July 28, 2008
MathSciNet review: 2431055
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps $ W^{1,p}(\mathbb{R}) \times W^{1,q}(\mathbb{R}) \to W^{1,r}(\mathbb{R})$ with $ 1 <p,q < \infty$ and $ r\geq 1$, boundedly and continuously. The same result holds on $ \mathbb{R}^n$ when $ r>1$. We also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B25, 54C08, 46E35

Retrieve articles in all journals with MSC (2000): 42B25, 54C08, 46E35


Additional Information

Emanuel Carneiro
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712-1082.
Email: ecarneiro@math.utexas.edu

Diego Moreira
Affiliation: Department of Mathematics, University of Iowa, Iowa City, Iowa 52242
Email: dmoreira@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09515-4
PII: S 0002-9939(08)09515-4
Keywords: Maximal operator, bilinear maximal, Sobolev spaces, weak differentiability, weak continuity
Received by editor(s): November 20, 2007
Published electronically: July 28, 2008
Additional Notes: The first author was supported by CAPES/FULBRIGHT grant BEX 1710-04-4.
Communicated by: Michael T. Lacey
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.