A geometrical version of Hardy's inequality for

Author:
Jesper Tidblom

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2265-2271

MSC (2000):
Primary 35P99; Secondary 35P20, 47A75, 47B25

DOI:
https://doi.org/10.1090/S0002-9939-04-07526-4

Published electronically:
March 25, 2004

MathSciNet review:
2052402

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Abstract: The aim of this article is to prove a Hardy-type inequality, concerning functions in for some domain , involving the volume of and the distance to the boundary of . The inequality is a generalization of a recently proved inequality by M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and A. Laptev (2002), which dealt with the special case .

**1.**G. Barbatis, S. Filippas, and A. Tertikas,*A unified approach to improved Hardy inequalities with best constants*, preprint, December 2000.**2.**H. Brezis and M. Marcus,*Hardy's inequalities revisited*, dedicated to Ennio De Giorgi, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) vol. 25 (1997) no. 1-2 (1998), pp. 217-237. MR**99m:46075****3.**E. B. Davies,*A review of Hardy inequalities*, Oper. Theory Adv. Appl., vol. 110 (1998), pp. 55-67. MR**2001f:35166****4.**E. B. Davies,*Heat kernels and spectral theory*, Cambridge University Press, Cambridge, 1989. MR**92a:35035****5.**E. B. Davies,*The Hardy constant*, Quart. J. Math. Oxford (2), vol. 46 (1995), pp. 417-431. MR**97b:46041****6.**E. B. Davies,*Spectral theory and differential operators*, Cambridge Studies in Advanced Mathematics, vol. 42, Cambridge University Press, Cambridge, 1995. MR**96h:47056****7.**G. Hardy, J. E. Littlewood, and G. Pólya,*Inequalities*, second edition, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1952. MR**13:727e****8.**G. Hardy,*Note on a theorem of Hilbert*, Math. Zeitschrift (6) (1920), pp. 314-317.**9.**M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, and A. Laptev,*A geometrical version of Hardy's inequality*, J. Funct. Anal. 189 (2002), no. 2, 539-548. MR**2003c:26022****10.**E. H. Lieb and M. Loss,*Analysis*, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 1997. MR**98b:00004****11.**T. Matskewich and P. E. Sobolevskii,*The best possible constant in a generalized Hardy's inequality for convex domains in*, Nonlinear Anal., vol. 28 (1997), pp. 1601-1610. MR**98a:26019****12.**V. G. Maz'ja,*Sobolev Spaces*, Springer-Verlag, Berlin, 1985. MR**87g:46056****13.**B. Opic and A. Kufner,*Hardy-type inequalities*, Pitman Research Notes in Mathematics Series, vol. 219, Longman Group UK Limited, London, 1990. MR**92b:26028**

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Additional Information

**Jesper Tidblom**

Affiliation:
Department of Mathematics, University of Stockholm, 106 91 Stockholm, Sweden

Email:
jespert@math.su.se

DOI:
https://doi.org/10.1090/S0002-9939-04-07526-4

Received by editor(s):
January 28, 2002

Published electronically:
March 25, 2004

Communicated by:
Jonathan M. Borwein

Article copyright:
© Copyright 2004
American Mathematical Society