Metric Sobolev spaces

 Access to full text

 Full (PDF)

1. Cheeger J., Differentiability of Lipschitz functions on metric measure spaces, Geom. Funct. Anal. 9 (1999), 428–517. Zbl 0942.58018, MR 2000g:53043. (1999) Zbl0942.58018MR1708448
2. Franchi B., Hajłasz P., Koskela P., Definitions of Sobolev classes on metric spaces, Ann. Inst. Fourier (Grenoble) 49 (1999), 1903–1924. Zbl 0938.46037, MR 2001a:46033. (1999) Zbl0938.46037MR1738070
3. Hajłasz P., Koskela P., Sobolev meets Poincaré, C. R. Acad. Sci. Paris, Sér. I Math. 320 (1995), 1211–1215. Zbl 0837.46024, MR 96f:46062. (1995) MR1336257
4. Hajłasz P., Koskela P., Sobolev met Poincaré, Mem. Amer. Math. Soc. 145 (2000). Zbl 0954.46022, MR 2000j:46063. MR1683160
5. Heinonen J., Koskela P., Quasiconformal maps in metric spaces with controlled geometry, Acta Math. 181 (1998), 1–61. Zbl 0915.30018, MR 99j:30025. (1998) Zbl0915.30018MR1654771
6. Heinonen J., Koskela P., Shanmuganlingam N., Tyson J., Sobolev spaces on metric measure spaces: an approach based on upper gradients, (in preparation). 
7. Keith S., A differentiable structure for metric measure spaces, Advances Math. (to appear). Zbl1077.46027MR2703118
8. Keith S., Modulus and the Poincaré inequality on metric measure spaces, Math. Z. (to appear). Zbl1037.31009MR2013501
9. Keith S., Rajala K., A remark on Poincaré inequalities on metric measure spaces, Preprint. Zbl1070.31003MR2098359
10. Koskela P., Onninen J., Sharp inequalities via truncation, J. Math. Anal. Appl. 278 (2003), 324–334. Zbl1019.26003MR1974010
11. Liu Y., Lu G., Wheeden R. L., Some equivalent definitions of high order Sobolev spaces on stratified groups and generalizations to metric spaces, Math. Ann. 323 (2002), 157–174. Zbl 1007.46034, MR 2003f:46048. Zbl1007.46034MR1906913
12. Lu G., Wheeden R. L., High order representation formulas and embedding theorems on stratified groups and generalizations, Studia Math. 142 (2000), 101–133. Zbl 0974.46039, MR 2001k:46055. Zbl0974.46039MR1792599
13. Malý J., Pick L., The sharp Riesz potential estimates in metric spaces, Indiana Univ. Math. J. 51 (2002), 251–268. Zbl pre01780940, MR 2003d:46045. Zbl1038.46027MR1909289
14. Rissanen J., Wavelets on self-similar sets and the structure of the spaces $M^{1,p}(E,\mu )$, Ann. Acad. Sci. Fenn. Math. Diss. 125 (2002). Zbl 0993.42016, MR 2002k:42081. MR1880640
15. Semmes S., Some novel types of fractal geometry, Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 2001.Zbl 0970.28001, MR 2002h:53073. Zbl0970.28001MR1815356
16. Shanmugalingam N., Newtonian spaces: an extension of Sobolev spaces to metric measure spaces, Rev. Mat. Iberoamericana 16 (2000), 243–279. Zbl 0974.46038, MR 2002b:46059. Zbl0974.46038MR1809341