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 
 

 

Weighted Hardy inequalities beyond Lipschitz domains


Author: Juha Lehrbäck
Journal: Proc. Amer. Math. Soc. 142 (2014), 1705-1715
MSC (2010): Primary 26D15, 46E35
DOI: https://doi.org/10.1090/S0002-9939-2014-11904-6
Published electronically: February 7, 2014
MathSciNet review: 3168477
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is a well-known fact that in a Lipschitz domain $ \Omega \subset \mathbb{R}^n$, a
$ p$-Hardy inequality, with weight $ \operatorname {dist}(x,\partial \Omega )^\beta $, holds for all $ u\in C_0^\infty (\Omega )$ whenever $ \beta <p-1$. We show that actually the same is true under the sole assumption that the boundary of the domain satisfies a uniform density condition with the exponent $ \lambda =n-1$. Corresponding results also hold for smaller exponents, and, in fact, our methods work in general metric spaces satisfying standard structural assumptions.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 26D15, 46E35

Retrieve articles in all journals with MSC (2010): 26D15, 46E35


Additional Information

Juha Lehrbäck
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), University of Jyväskylä, FIN-40014, Finland
Email: juha.lehrback@jyu.fi

DOI: https://doi.org/10.1090/S0002-9939-2014-11904-6
Received by editor(s): March 12, 2012
Received by editor(s) in revised form: June 21, 2012
Published electronically: February 7, 2014
Additional Notes: The author was supported in part by the Academy of Finland, grant no. 120972
Communicated by: Jeremy Tyson
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.