On the hypoellipticity for infinitely degenerate semi-elliptic operators

Yoshinori MORIMOTO

doi:10.2969/jmsj/03020327

Yoshinori MORIMOTO

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JOURNAL FREE ACCESS

1978 Volume 30 Issue 2 Pages 327-358

DOI https://doi.org/10.2969/jmsj/03020327

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Published: 1978 Received: October 18, 1976 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: CITATION Details: Wrong : 1) R. Beals, Spatial inhomogeneous pseudo-differential operators, III, (to appear).
2) A.P. Calderón and R. Vaillancourt, A class of bounded pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A., 69 (1972), 1185-1187.
3) Yu. V. Egorov, Subelliptic operators, Uspehi Mat. Nauk, 30: 2 (1975), 57-114=Russian Math. Surveys, 30: 2 (1975), 59-118.
4) Yu. V. Egorov, On subelliptic operators, Uspehi Mat. Nauk, 30: 3 (1975), 57-104 =Russian Math. Surveys, 30: 3 (1975).
5) V.S. Fedii, On a criterion for hypoellipticity, Mat. Sb., 85 (1971), 18-48=Math. USSR Sb., 14 (1971), 15-45.
6) V.V. Grushin, On a class of hypoelliptic operators, Mat. Sb., 83 (1970), 456-473=Math. USSR Sb., 12 (1970), 458-476.
7) V.V. Grushin, Hypoelliptic differential equations and pseudodifferential operators with operator valued symbols, Mat. Sb., 88 (1972), 504-521=Math. USSR Sb., 17 (1972), 497-514.
8) L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Symposium on Singular Integrals, Amer. Math. Soc., 10 (1967), 138-183.
9) L. Hörmander, Hypoelliptic second order differential equations, Acta Math., 119 (1967), 147-171.
10) L. Hörmander, A class of hypoelliptic operator with double characteristics, Math. Ann., 217 (1975), 165-188.
11) Y. Kato, On a class of hypoelliptic differential operators, Proc. Japan Acad., 49 (1970), 33-37.
12) H. Kumano-go, Algebras of pseudo-differential operators, J, Fac. Sci. Univ. Tokyo, 17 (1970), 31-50.
13) H. Kumano-go, Pseudo-differential operators, Iwanami Publisher, Tokyo, 1974 (in Japanese).
14) H. Kumano-go, Pseudo-differential operators of multiple symbol and the Calderón-Vaillancourt theorem, J. Math. Soc. Japan, 27 (1975), 113-120.
15) H. Kumano-go and K. Taniguchi, Oscillatory integrals of symbols of pseudo-differential operators on Rⁿ and operators of Fredholm type, Proc. Japan Acad., 49 (1973), 397-402.
16) O.A. Oleinik and E.V. Radkevich, Second order equations with non-negative characteristic form, Amer. Math. Soc., Providence, Rhode Island and Plenum Press, 1973.
17) K. Taniguchi, On the hypoellipticity of the operator a(x, D_x)+g(x)b(x, y, D_y), Math. Japon., 20 (1976), 301-320.
18) F. Treves, An invariant criterion of hypoellipticity, Amer. J. Math., 83 (1961), 645-668.
19) C. Tsutsumi, Parametrices for degenerate operators of Grushin's type, (to appear).

Right : [1] R. Beals, Spatial inhomogeneous pseudo-differential operators, III, (to appear).
[2] A. P. Calderón and R. Vaillancourt, A class of bounded pseudodifferential operators, Proc. Nat. Acad. Sci. U. S. A., 69 (1972), 1185-1187.
[3] Yu. V. Egorov, Subelliptic operators, Uspehi Mat. Nauk, 30: 2 (1975), 57-114=Russian Math. Surveys, 30: 2 (1975), 59-118.
[4] Yu. V. Egorov, On subelliptic operators, Uspehi Mat. Nauk, 30: 3 (1975), 57-104=Russian Math. Surveys, 30: 3 (1975).
[5] V. S. Fedii, On a criterion for hypoellipticity, Mat. Sb., 85 (1971), 18-48=Math. USSR Sb., 14 (1971), 15-45.
[6] V. V. Grushin, On a class of hypoelliptic operators, Mat. Sb., 83 (1970), 456-473=Math. USSR Sb., 12 (1970), 458-476.
[7] V. V. Grushin, Hypoelliptic differential equations and pseudodifferential operators with operator valued symbols, Mat. Sb., 88 (1972), 504-521=Math. USSR Sb., 17 (1972), 497-514.
[8] L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Symposium on Singular Integrals, Amer. Math. Soc., 10 (1967), 138-183.
[9] L. Hörmander, Hypoelliptic second order differential equations, Acta Math., 119 (1967), 147-171.
[10] L. Hörmander, A class of hypoelliptic operator with double characteristics, Math. Ann., 217 (1975), 165-188.
[11] Y. Kato, On a class of hypoelliptic differential operators, Proc. Japan Acad., 49 (1970), 33-37.
[12] H. Kumano-go, Algebras of pseudo-differential operators, J, Fac. Sci. Univ. Tokyo, 17 (1970), 31-50.
[13] H. Kumano-go, Pseudo-differential operators, Iwanami Publisher, Tokyo, 1974 (in Japanese).
[14] H. Kumano-go, Pseudo-differential operators of multiple symbol and the Calderón-Vaillancourt theorem, J. Math. Soc. Japan, 27 (1975), 113-120.
[15] H. Kumano-go and K. Taniguchi, Oscillatory integrals of symbols of pseudodifferential operators on Rⁿ and operators of Fredholm type, Proc. Japan Acad., 49 (1973), 397-402.
[16] O. A. Oleinik and E. V. Radkevich, Second order equations with non-negative characteristic form, Amer. Math. Soc., Providence, Rhode Island and Plenum Press, 1973.
[17] K. Taniguchi, On the hypoellipticity of the operator a(x,D_x)+g(x)b(x,y,D_y), Math. Japon., 20 (1976), 301-320.
[18] F. Treves, An invariant criterion of hypoellipticity, Amer. J. Math., 83 (1961), 645-668.
[19] C. Tsutsumi, Parametrices for degenerate operators of Grushin's type, (to appear).

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