Proceedings of the American Mathematical Society

Author(s): Pekka Koskela; Xiao Zhong
Journal: Proc. Amer. Math. Soc. 131 (2003), 1151-1158.
MSC (2000): Primary 26D10, 31C99, 46E35
Posted: July 26, 2002
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Abstract: We establish a self-improving property of the Hardy inequality and an estimate on the size of the boundary of a domain supporting a Hardy inequality.

1.: H. Aikawa and M. Essén, Potential theory--selected topics, Lecture Notes in Mathematics, 1663, Springer-Verlag, Berlin, 1996. MR 98f:31005
2.: A. Ancona, On strong barriers and an inequality of Hardy for domains in ${\mathbf R}^n$ , J. London Math. Soc. (2) 34 (1986), 274-290. MR 87k:31004
3.: J. Björn, P. MacManus, N. Shanmugalingam, Fat sets and Hardy inequalities in metric spaces, J. Anal. Math. 85 (2001), 339-369.
4.: M. Bourdon and H. Pajot, Poincaré inequalities and quasiconformal structures on the boundary of some hyperbolic buildings, Proc. Amer. Math. Soc. 127 (1999), 2315-2324. MR 99j:30024
5.: D. Danielli, N. Garofalo and Duy-Minh, Nhieu, Trace inequalities for Carnot-Caratheodory spaces and applications, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 27 (1998), 195-252. MR 2000d:46039
6.: P. Haj $\l$ asz and P. Koskela, Sobolev met Poincaré, Mem. Amer. Math. Soc. 145 (2000), no. 688, 101 pp. MR 2000j:46063
7.: J. Heinonen and P. Koskela, Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), 1-61. MR 99j:30025
8.: J. Kinnunen and O. Martio, The Sobolev capacity on metric spaces, Ann. Acad. Sci. Fenn. Math. (2) 21 (1996), 367-382. MR 98c:46063
9.: A. Kufner, Weighted Sobolev spaces, Teubner-texte, 1980, 2nd ed. MR 84e:46029
10.: T. J. Laakso, Ahlfors Q-regular spaces with arbitrary Q admitting a weak Poincaré inequality, Geom. Funct. Anal. 10 (2000), 111-123. MR 2001m:30027
11.: J.L. Lewis, Uniformly fat sets, Trans. Amer. Math. Soc. 308 (1988), 177-196. MR 89e:31012
12.: J.L. Lewis, On very weak solutions of certain elliptic systems, Comm. P. D. E. 18 (1993), 1515-1537. MR 94g:35087
13.: V. G. Maz'ya, Sobolev spaces, Springer-Verlag, Berlin - New York, 1985.
14.: J.D. Strömberg and A. Torchinsky, Weighted Hardy Spaces, Lecture Notes in Math., 1381, Springer-Verlag, Berlin - New York, 1989. MR 90j:42053
15.: A. Wannebo, Hardy inequalities, Proc. Amer. Math. Soc. 109 (1990), 85-95. MR 90h:26025

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 26D10, 31C99, 46E35

Pekka Koskela
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, Fin-40351 Jyväskylä, Finland
Email: pkoskela@math.jyu.fi

Xiao Zhong
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, Fin-40351 Jyväskylä, Finland
Email: zhong@math.jyu.fi

DOI: 10.1090/S0002-9939-02-06711-4
PII: S 0002-9939(02)06711-4
Received by editor(s): May 30, 2001
Received by editor(s) in revised form: November 5, 2001
Posted: July 26, 2002
Additional Notes: This research was partially supported by the Academy of Finland, projects 39788 and 41964, and the foundation Vilho, Yrjö ja Kalle Väisälän rahasto (X.Z.). Part of this research was done while the second author was visiting at the Mittag-Leffler Institute. He wishes to thank the Institute for their support and hospitality.
Communicated by: Juha M. Heinonen
Copyright of article: Copyright 2002, American Mathematical Society

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