Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Pointwise Hardy inequalities and uniformly fat sets

Author(s): Juha Lehrbäck
Journal: Proc. Amer. Math. Soc. 136 (2008), 2193-2200.
MSC (2000): Primary 46E35, 31C15; Secondary 26D15, 42B25
Posted: January 17, 2008
MathSciNet review: 2383525
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: We prove that it is equivalent for domain in $\mathbb{R}^n$ to admit the pointwise -Hardy inequality, have uniformly -fat complement, or satisfy a uniform inner boundary density condition.

References:

1.: A. ANCONA, `On strong barriers and an inequality of Hardy for domains in $\mathbb{R}\sp n$ ', J. London Math. Soc. (2) 34 (1986), no. 2, 274-290. MR 856511 (87k:31004)
2.: P. HAJłASZ, `Pointwise Hardy inequalities', Proc. Amer. Math. Soc. 127 (1999), no. 2, 417-423. MR 1458875 (99c:46028)
3.: G. H. HARDY, J. E. LITTLEWOOD AND G. P´OLYA, `Inequalities' (Second edition), Cambridge, at the University Press, 1952. MR 0046395 (13:727e)
4.: J. HEINONEN, T. KILPELÄINEN AND O. MARTIO, `Nonlinear potential theory of degenerate elliptic equations', Oxford University Press, 1993. MR 1207810 (94e:31003)
5.: J. HEINONEN AND P. KOSKELA, `Quasiconformal maps in metric spaces with controlled geometry', Acta Math. 181 (1998), no. 1, 1-61. MR 1654771 (99j:30025)
6.: J. KINNUNEN AND O. MARTIO, `Hardy's inequalities for Sobolev functions', Math. Res. Lett. 4 (1997), no. 4, 489-500. MR 1470421 (98k:46052)
7.: P. KOSKELA AND X. ZHONG, `Hardy's inequality and the boundary size', Proc. Amer. Math. Soc. 131 (2003), no. 4, 1151-1158. MR 1948106 (2004e:26021)
8.: J. L. LEWIS, `Uniformly fat sets', Trans. Amer. Math. Soc. 308 (1988), no. 1, 177-196. MR 946438 (89e:31012)
9.: J. NEˇCAS, `Sur une méthode pour résoudre les équations aux dérivées partielles du type elliptique, voisine de la variationnelle', Ann. Scuola Norm. Sup. Pisa (3) 16 (1962) 305-326. MR 0163054 (29:357)
10.: E. M. STEIN, `Singular integrals and differentiability properties of functions', Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095 (44:7280)
11.: A. WANNEBO, `Hardy inequalities', Proc. Amer. Math. Soc. 109 (1990), 85-95. MR 1010807 (90h:26025)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 46E35, 31C15, 26D15, 42B25

Retrieve articles in all Journals with MSC (2000): 46E35, 31C15, 26D15, 42B25

Additional Information:

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

DOI: 10.1090/S0002-9939-08-09261-7
PII: S 0002-9939(08)09261-7
Received by editor(s): May 16, 2007
Posted: January 17, 2008
Additional Notes: The author was supported in part by the Academy of Finland.
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|