Measures of finite (r,p)-energy and potentials on a separable metric space
Séminaire de probabilités de Strasbourg, Volume 26 (1992), p. 415-444
@article{SPS_1992__26__415_0,
     author = {Kazumi, Tetsuya and Shigekawa, Ichiro},
     title = {Measures of finite (r,p)-energy and potentials on a separable metric space},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     publisher = {Springer - Lecture Notes in Mathematics},
     volume = {26},
     year = {1992},
     pages = {415-444},
     zbl = {0769.60069},
     mrnumber = {1232008},
     language = {en},
     url = {http://www.numdam.org/item/SPS_1992__26__415_0}
}
Kazumi, Tetsuya; Shigekawa, Ichiro. Measures of finite (r,p)-energy and potentials on a separable metric space. Séminaire de probabilités de Strasbourg, Volume 26 (1992) pp. 415-444. http://www.numdam.org/item/SPS_1992__26__415_0/

[1] S. Albeverio and M. Röckner, Classical Dirichlet forms on topological vector spaces- the construction of the associated diffusion process, Probab. Th. Rel. Fields, 83 (1989), 405-434. | MR 1017404 | Zbl 0661.60094

[2] S. Albeverio, M. Fukushima, W. Hansen, Z.M. Ma and M. Röckner, An invariance result for capacities on Wiener space, preprint. | MR 1163462 | Zbl 0786.31008

[3] N. Bourbaki, "Topologie générale," Chapitres 5 à 10, Hermann, Paris, 1974. | Zbl 0337.54001

[4] E.B. Davies, "One-parameter semigroups , "Academic Press, London, 1980. | MR 591851 | Zbl 0457.47030

[5] N. Dunford and J.T. Schwartz, "Linear operators," Part I Interscience Publishers, New York. | MR 117523 | Zbl 0084.10402

[6] S.N. Ethier and T.G. Kurtz, "Markov processes," John Wiley & Sons, New York, 1986. | MR 838085 | Zbl 0592.60049

[7] D. Feyel and A. De La Pradelle, Espaces de Sobolev gaussiens, Ann. Inst. Fourier, Grenoble, 39 (1989), 875-908. | Numdam | MR 1036336 | Zbl 0664.46028

[8] D. Feyel and A. De La Pradelle, Capacités gaussiennes, Ann. Inst. Fourier, Grenoble, 41 (1991), 49-76. | Numdam | MR 1112191 | Zbl 0735.46018

[9] D. Feyel and A. De La Pradelle, Opérateurs linéaires gaussiens, preprint | MR 1293754 | Zbl 0825.46013

[10] M. Fukushima, "Dirichlet forms and Markov Processes," North Holland/ Kodansha, Amsterdam/Tokyo, 1980. | MR 569058 | Zbl 0422.31007

[11] M. Fukushima and H. Kaneko, On (r,p)-capacities for general Markovian semigroups, in "Infinite dimensional analysis and stochastic processes, " ed. by S. Albeverio, Pitman, 1985. | MR 865017 | Zbl 0573.60069

[12] H. Kaneko, On (r,p)-capacities for Markov processes, Osaka J. Math., 23 (1986), 325-336. | MR 856891 | Zbl 0633.60090

[13] S. Kusuoka, Dirichlet forms and diffusion processes on Banach space, J. Fac. Science Univ. Tokyo, Sec. 1A 29 (1982), 79-95. | MR 657873 | Zbl 0496.60079

[14] V.G. Maz'Ya and V.P. Khavin, Non-linear potential theory, Russian Math. Surveys, 27 (1983), 71-148. | Zbl 0269.31004

[15] L.H. Loomis, "An introduction to abstract harmonic analysis," D. Van Nostrand, Princeton, N. J., 1953. | MR 54173 | Zbl 0052.11701

[16] P.A. Meyer, "Probability and Potential , "Blaisdell Publishing Co., Waltham, Massachusetts, 1966 | MR 205288 | Zbl 0138.10401

[17] H.H. Schaefer, "Topological vector spaces," Springer, New York-Heidelberg-Berlin, 1971. | MR 342978 | Zbl 0217.16002

[18] B. Schmuland, An alternative compactification for classical Dirichlet forms on topological vector spaces, Stochastics, 33 (1990), 75-90. | MR 1079933 | Zbl 0726.31008

[19] I. Shigekawa, Sobolev spaces over the Wiener space based on an Ornstein-Uhlenbeck operator, preprint. | MR 1194112

[20] E.M. Stein, "Topics in harmonic analysis related to Littlewood-Paley theory," Annals of Math. Study no. 63, Princeton, 1970. | MR 252961 | Zbl 0193.10502

[21] H. Sugita, Sobolev spaces of Wiener functionals and Malliavin's calculus, J. Math. Kyoto Univ., 25 (1985), 31-48. | MR 777244 | Zbl 0581.46026

[22] H. Sugita, Positive generalized Wiener functions and potential theory over abstract Wiener spaces, Osaka J. Math., 25 (1988), 665-696. | MR 969026 | Zbl 0737.46038

[23] M. Takeda, (r,p)-capacity on the Wiener space and properties of Brownian motion, Z. Wahr. verw. Gebiete, 68 (1984), 149-162. | MR 767798 | Zbl 0573.60068