Pointwise Hardy inequalities and uniformly fat sets
HTML articles powered by AMS MathViewer
- by Juha Lehrbäck PDF
- Proc. Amer. Math. Soc. 136 (2008), 2193-2200 Request permission
Abstract:
We prove that it is equivalent for domain in $\mathbb {R}^n$ to admit the pointwise $p$-Hardy inequality, have uniformly $p$-fat complement, or satisfy a uniform inner boundary density condition.References
- Alano Ancona, On strong barriers and an inequality of Hardy for domains in $\textbf {R}^n$, J. London Math. Soc. (2) 34 (1986), no. 2, 274–290. MR 856511, DOI 10.1112/jlms/s2-34.2.274
- Piotr Hajłasz, Pointwise Hardy inequalities, Proc. Amer. Math. Soc. 127 (1999), no. 2, 417–423. MR 1458875, DOI 10.1090/S0002-9939-99-04495-0
- G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge, at the University Press, 1952. 2d ed. MR 0046395
- Juha Heinonen, Tero Kilpeläinen, and Olli Martio, Nonlinear potential theory of degenerate elliptic equations, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1993. Oxford Science Publications. MR 1207810
- Juha Heinonen and Pekka Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), no. 1, 1–61. MR 1654771, DOI 10.1007/BF02392747
- Juha Kinnunen and Olli Martio, Hardy’s inequalities for Sobolev functions, Math. Res. Lett. 4 (1997), no. 4, 489–500. MR 1470421, DOI 10.4310/MRL.1997.v4.n4.a6
- Pekka Koskela and Xiao Zhong, Hardy’s inequality and the boundary size, Proc. Amer. Math. Soc. 131 (2003), no. 4, 1151–1158. MR 1948106, DOI 10.1090/S0002-9939-02-06711-4
- John L. Lewis, Uniformly fat sets, Trans. Amer. Math. Soc. 308 (1988), no. 1, 177–196. MR 946438, DOI 10.1090/S0002-9947-1988-0946438-4
- Jindřich Nečas, Sur une méthode pour résoudre les équations aux dérivées partielles du type elliptique, voisine de la variationnelle, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 16 (1962), 305–326 (French). MR 163054
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- Andreas Wannebo, Hardy inequalities, Proc. Amer. Math. Soc. 109 (1990), no. 1, 85–95. MR 1010807, DOI 10.1090/S0002-9939-1990-1010807-1
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
- Received by editor(s): May 16, 2007
- Published electronically: January 17, 2008
- Additional Notes: The author was supported in part by the Academy of Finland.
- Communicated by: Juha M. Heinonen
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 2193-2200
- MSC (2000): Primary 46E35, 31C15; Secondary 26D15, 42B25
- DOI: https://doi.org/10.1090/S0002-9939-08-09261-7
- MathSciNet review: 2383525