Geodesic
The Poincaré Inequality and Reverse Doubling Weights
Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 206-214

Voir la notice de l'article provenant de la source Cambridge University Press

We show that Poincaré inequalities with reverse doubling weights hold in a large class of irregular domains whenever the weights satisfy certain conditions. Examples of these domains are John domains.
DOI : 10.4153/CMB-2004-020-4
Mots-clés : 46E35, reverse doubling weights, Poincaré inequality, John domains 
Hurri-Syrjänen, Ritva. The Poincaré Inequality and Reverse Doubling Weights. Canadian mathematical bulletin, Tome 47 (2004) no. 2, pp. 206-214. doi: 10.4153/CMB-2004-020-4
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[1] [1] Bojarski, B., Remarks on Sobolev imbedding inequalities. Complex Analysis, Joensuu 1987, Lecture Notes in Math. 1351, Springer, Berlin, 1988, 52–68. Google Scholar

[2] [2] Hurri-Syrjänen, R., Unbounded Poincaré domains. Ann. Acad. Sci. Fenn. Ser. A I Math. 17 (1992), 409–423. Google Scholar

[3] [3] Jones, P. W., Quasiconformal mappings and extendability of functions in Sobolev spaces. Acta Math. 147 (1981), 71–88. Google Scholar

[4] [4] Martio, O., John domains, bilipschitz balls and Poincaré inequality. Rev. RoumaineMath. Pures Appl. 33 (1988), 107–112. Google Scholar

[5] [5] Martio, O. and Sarvas, J., Injectivity theorems in plane and space. Ann. Acad. Sci. Fenn. Ser. A I Math. 4(1978–1979), 383–401. Google Scholar

[6] [6] Näkki, R. and Väisälä, J., John disks. Exposition. Math. 9 (1991), 3–43. Google Scholar

[7] [7] Sawyer, E. and Wheeden, R., Weighted inequalities for fractional integrals on euclidean and homogeneous spaces. Amer. J. Math. 114 (1992), 813–874. Google Scholar

[8] [8] Stein, E. M., Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, NJ, 1970. Google Scholar

[9] [9] Väisälä, J., Quasiconformal maps of cylindrical domains. Acta Math. 162 (1989), 201–225. Google Scholar

[10] [10] Väisälä, J., Exhaustions of John domains. Ann. Acad. Sci. Fenn. Ser. A I Math. 19 (1994), 47–57. Google Scholar

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