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An extension of Hörmander’s theorem for infinitely degenerate second-order operators
Denis R. Bell and Salah-Eldin A. Mohammed
Source: Duke Math. J. Volume 78, Number 3
(1995), 453-475.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077285944
Mathematical Reviews number (MathSciNet): MR1334203
Zentralblatt MATH identifier: 0840.60053
Digital Object Identifier: doi:10.1215/S0012-7094-95-07822-3
References
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[BM] D. R. Bell and S.-E. A. Mohammed, Hypoelliptic parabolic operators with exponential degeneracies, C. R. Acad. Sci. Paris Sér. I Math. 317 (1993), no. 11, 1059–1064.
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[H] L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171.
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[IW] N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, North-Holland Mathematical Library, vol. 24, North-Holland Publishing Co., Amsterdam, 1989.
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[KS] S. Kusuoka and D. Stroock, Applications of the Malliavin calculus. II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985), no. 1, 1–76.
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[M1] P. Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Res. Inst. Math. Sci., Kyoto Univ., Kyoto, 1976), Wiley, New York, 1978, pp. 195–263.
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[M2] P. Malliavin, $C\spk$-hypoellipticity with degeneracy. II, Stochastic analysis (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1978), Academic Press, New York, 1978, pp. 327–340.
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[Mo] Y. Morimoto, Hypoellipticity for infinitely degenerate elliptic operators, Osaka J. Math. 24 (1987), no. 1, 13–35.
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[N] J. Norris, Simplified Malliavin calculus, Séminaire de Probabilités, XX, 1984/85, Lecture Notes in Math., vol. 1204, Springer, Berlin, 1986, pp. 101–130.
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[OR] O. A. Oleĭ nik and E. V. Radkevič, Second order equations with nonnegative characteristic form, Plenum Press, New York, 1973.
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[S] D. Stroock, The Malliavin calculus, a functional analytic approach, J. Funct. Anal. 44 (1981), no. 2, 212–257.
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Digital Object Identifier: doi:10.1016/0022-1236(81)90011-2
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