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2000 | 74 | 1 | 97-103
Tytuł artykułu

How to get rid of one of the weights in a two-weight Poincaré inequality?

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that if a Poincaré inequality with two different weights holds on every ball, then a Poincaré inequality with the same weight on both sides holds as well.
Rocznik
Tom
74
Numer
1
Strony
97-103
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-04-30
poprawiono
1999-07-20
Twórcy
  • Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato, 5, I-40127 Bologna, Italy
  • Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
Bibliografia
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  • [4] J. Boman, $L^p$-estimates for very strongly elliptic systems, report no 29, Dept. of Math., Univ. of Stockholm, 1982.
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  • [7] S. K. Chua, Weighted Sobolev inequalities on domains satisfying the chain condition, Proc. Amer. Math. Soc. 117 (1993), 449-457.
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  • [9] B. Franchi, C. E. Gutiérrez and R. L. Wheeden, Weighted Sobolev-Poincaré inequalities for Grushin type operators, Comm. Partial Differential Equations 19 (1994), 523-604.
  • [10] B. Franchi, P. Hajłasz and P. Koskela, Definitions of Sobolev classes on metric spaces, Ann. Inst. Fourier (Grenoble) 49 (1999), 1903-1924.
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  • [12] B. Franchi, G. Lu and R. L. Wheeden, Representation formulas and weighted Poincaré inequalities for Hörmander vector fields, Ann. Inst. Fourier (Grenoble) 45 (1995), 577-604.
  • [13] B. Franchi, G. Lu and R. L. Wheeden, A relationship between Poincaré-type inequalities and representation formulas in spaces of homogeneous type, Internat. Mat. Res. Notices 1996, no. 1, 1-14.
  • [14] B. Franchi, C. Pérez and R. L. Wheeden, Self-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous type, J. Funct. Anal. 153 (1998), 108-146.
  • [15] B. Franchi, C. Pérez and R. L. Wheeden, in preparation.
  • [16] B. Franchi and R. L. Wheeden, Some remarks about Poincaré type inequalities and representation formulas in metric spaces of homogeneous type, J. Inequalities Appl. 3 (1999), 65-89
  • [17] B. Franchi and R. L. Wheeden, Compensation couples and isoperimetric estimates for vector fields, Colloq. Math. 74 (1997), 1-27.
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  • [19] N. Garofalo and D. M. Nhieu, Isoperimetric and Sobolev inequalities for Carnot-Carathéodory spaces and the existence of minimal surfaces, Comm. Pure Appl. Math. 49 (1996), 1081-1144.
  • [20] P. Hajłasz, Sobolev spaces on an arbitrary metric space, Potential Anal. 5 (1996), 403-415.
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Typ dokumentu
Bibliografia
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