On hypoellipticity for a certain operator with double characteristic

Toshihiko HOSHIRO

doi:10.2969/jmsj/04330593

Toshihiko HOSHIRO

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 3 Pages 593-603

DOI https://doi.org/10.2969/jmsj/04330593

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Published: 1991 Received: May 22, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor Mutsuhide Matsumura on his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) L. Boutet de Monvel, Hypoelliptic operators with double characteristics and related pseudodifferential operators, Comm. Pure and Appl. Math., 27 (1974), 585-639.
2) G. B. Folland, Harmonic analysis in phase space, Ann. of Math. Studies 122, Princeton Univ. Press, 1989.
3) A. Grigis, Hypoellipticité et parametrixes pour des opérateurs pseudodifférentiels à caracteristiques doubles, Astérisque, 34-35 (1976), 183-205.
4) A. Grigis and L. P. Rothschild, A criterion for analytic hypoellipticity of a class of differential operators with polynomial coefficients, Ann. of Math., 118 (1983), 443-460.
5) V. V. Grušin, On a class of hypoelliptic operators degenerating on a manifold, Math. USSR Sb., 13(1971), 155-185.
6) B. Helffer, Sur l'hypoellipticité des opérateurs pseudodifférentiels à caractéristiques multiples (perte de 3/2 dérivées), Bull. Soc. Math. France mémoire, 51-52 (1977), 13-61.
7) L. Hörmander, The analysis of linear partial differential operators I, Springer, 1983.
8) T. Hoshiro, Micro-local energy method of Mizohata and hypoellipticity, J. Math. Kyoto Univ., 28 (1988), 1-12.
9) T. Hoshiro, Hypoellipticity for infinitely degenerate elliptic and parabolic operators of second order, J. Math. Kyoto Univ., 28 (1988), 615-632.
10) H. Kumano-go, Pseudo-differential operators, MIT Press, 1981.
11) K. H. Kwon, Hypoellipticity and local solvability of operators with double characteristics, Comm. P. D. E., 10 (1985), 525-542.
12) Y. Morimoto, Criteria for hypoellipticity of differential operators, Publ. Res. Inst. Math. Sci. Kyoto Univ., 22 (1986), 1129-1154.
13) E. M. Stein, An example on the Heisenberg group related to the Lewy operator, Invent. Math., 69(1982), 209-216.
14) K. Taira, Hypoelliptic differential operators with double characteristics, Proc. Japan Acad., 50(1974), 124-126.

Right : [1] L. Boutet de Monvel, Hypoelliptic operators with double characteristics and related pseudodifferential operators, Comm. Pure and Appl. Math., 27 (1974), 585-639.
[2] G. B. Folland, Harmonic analysis in phase space, Ann. of Math. Studies 122, Princeton Univ. Press, 1989.
[3] A. Grigis, Hypoellipticité et parametrixes pour des opérateurs pseudodifférentiels à caracteristiques doubles, Astérisque, 34-35 (1976), 183-205.
[4] A. Grigis and L. P. Rothschild, A criterion for analytic hypoellipticity of a class of differential operators with polynomial coefficients, Ann. of Math., 118 (1983), 443-460.
[5] V. V. Grušin, On a class of hypoelliptic operators degenerating on a manifold, Math. USSR Sb., 13 (1971), 155-185.
[6] B. Helffer, Sur l'hypoellipticité des opérateurs pseudodifférentiels à caractéristiques multiples (perte de 3/2 dérivées), Bull. Soc. Math. France mémoire, 51-52 (1977), 13-61.
[7] L. Hörmander, The analysis of linear partial differential operators I, Springer, 1983.
[8] T. Hoshiro, Micro-local energy method of Mizohata and hypoellipticity, J. Math. Kyoto Univ., 28 (1988), 1-12.
[9] T. Hoshiro, Hypoellipticity for infinitely degenerate elliptic and parabolic operators of second order, J. Math. Kyoto Univ., 28 (1988), 615-632.
[10] H. Kumano-go, Pseudo-differential operators, MIT Press, 1981.
[11] K. H. Kwon, Hypoellipticity and local solvability of operators with double characteristics, Comm. P. D. E., 10 (1985), 525-542.
[12] Y. Morimoto, Criteria for hypoellipticity of differential operators, Publ. Res. Inst. Math. Sci. Kyoto Univ., 22 (1986), 1129-1154.
[13] E. M. Stein, An example on the Heisenberg group related to the Lewy operator, Invent. Math., 69 (1982), 209-216.
[14] K. Taira, Hypoelliptic differential operators with double characteristics, Proc. Japan Acad., 50 (1974), 124-126.

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