Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Maximal potentials, maximal singular integrals, and the spherical maximal function


Authors: Piotr Hajłasz and Zhuomin Liu
Journal: Proc. Amer. Math. Soc. 142 (2014), 3965-3974
MSC (2010): Primary 46E35; Secondary 42B20, 42B25
Published electronically: July 31, 2014
MathSciNet review: 3251736
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a notion of maximal potentials and we prove that they form bounded operators from $ L^p$ to the homogeneous Sobolev space $ \dot {W}^{1,p}$ for all $ n/(n-1)<p<n$. We apply this result to the problem of boundedness of the spherical maximal operator in Sobolev spaces.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46E35, 42B20, 42B25

Retrieve articles in all journals with MSC (2010): 46E35, 42B20, 42B25


Additional Information

Piotr Hajłasz
Affiliation: Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: hajlasz@pitt.edu

Zhuomin Liu
Affiliation: Department of Mathematics, 301 Thackeray Hall, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Address at time of publication: Department of Mathematics and Statistics, P. O. Box 35 (MaD), FI-40014 University of Jyväskylä, Finland
Email: liuzhuomin@hotmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-12129-0
Keywords: Sobolev spaces, potentials, singular integrals, spherical maximal function
Received by editor(s): November 3, 2012
Received by editor(s) in revised form: December 31, 2012
Published electronically: July 31, 2014
Additional Notes: The first author was supported by NSF grant DMS-0900871
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.