×

Subelliptic estimates and function spaces on nilpotent Lie groups. (English) Zbl 0312.35026


MSC:

35H10 Hypoelliptic equations
26A16 Lipschitz (Hölder) classes
35D10 Regularity of generalized solutions of PDE (MSC2000)
22E30 Analysis on real and complex Lie groups
43A80 Analysis on other specific Lie groups
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Bony, J. M., Principe du maximum, inégalité de Harnack, et unicité du probléme de Cauchy pour les operateurs elliptiques dégénérésAnn. Inst. Fourier Grenoble,19 (1) (1969), 277–304. · Zbl 0176.09703
[2] Calderón, A. P., Lebesgue spaces of differentiable functions and distributions,Proc. Symp. Pure Math.,4 (1961), 33–49. · Zbl 0195.41103
[3] Coifman, R. andWeiss, G. Analyse harmonique non-commutative sur certains espaces homogènes, Lecture notes #242, Springer-Verlag, Berlin, (1971).
[4] Dyer, J. L. A nilpotent Lie algebra with nilpotent automorphism group,Bull. Amer. Math. Soc.,76 (1970), 52–56. · Zbl 0198.05402
[5] Folland, G. B. andKohn, J. J. The Neumann problem for the Cauchy-Riemann complex, Ann. of Math. Studies #75, Princeton University Press, Princeton, (1972). · Zbl 0247.35093
[6] Folland, G. B. andStein, E. M. Parametrices and estimates for the 206-1 complex on strongly pseudoconvex boundaries.Bull. Amer. Math. Soc.,80 (1974), 253–258. · Zbl 0294.35059
[7] Folland, G. B. andStein, E. M. Estimates for the 206-2 complex and analysis on the Heisenberg group,Comm. Pure Appl. Math.,27 (1974), 429–522. · Zbl 0293.35012
[8] Guillemin, V. andSternberg, S. Subelliptic estimates for complexes,Proc. Nat. Acad. Sci. U.S.A.,67 (1970), 271–274. · Zbl 0202.20801
[9] Hochschild, G. The structure of Lie groups, Holden-Day, San Francisco, (1965). · Zbl 0131.02702
[10] Hörmander, L. Hypoelliptic second-order differential equations,Acta Math.,119 (1967), 147–171. · Zbl 0156.10701
[11] Hunt, G. A. Semigroups of measures on Lie groups,Trans. Amer. Math. Soc.,81 (1956), 264–293. · Zbl 0073.12402
[12] Jørgensen, P. Representations of differential operators on a Lie group, to appear. · Zbl 0311.43003
[13] Knapp, A. W. andStein, E. M. Intertwining operators for semi-simple groups,Ann. of Math.,93 (1971), 489–578. · Zbl 0257.22015
[14] Kohn, J. J. andNirenberg, L. Non-coercive boundary value problems,Comm. Pure Appl. Math.,18 (1965), 443–492. · Zbl 0125.33302
[15] Komatsu, H. Fractional powers of operators,Pac. J. Math.,19 (1966), 285–346. · Zbl 0154.16104
[16] Komatsu, H. Fractional powers of operators, II: Interpolation spaces,Pac. J. Math.,21 (1967), 89–111. · Zbl 0168.10702
[17] Komatsu, H. Fractional powers of operators, III: Negative powers,J. Math. Soc. Japan,21 (1969), 205–220. · Zbl 0181.41003
[18] Komatsu, H. Fractional powers of operators, IV: Potential operators,J. Math. Soc. Japan,21 (1969), 221–228. · Zbl 0181.41003
[19] Komatsu, H. Fractional powers of operators, V: Dual operators,J. Fac. Sci. Univ. Tokyo, Sec. IA,17 (1970), 373–396. · Zbl 0208.16302
[20] Komatsu, H. Fractional powers of operators, VI: Interpolation of nonnegative operators and imbedding theorems,J. Fac. Sci. Univ. Tokyo, Sec. IA,19 (1972), 1–62. · Zbl 0249.47013
[21] Korányi, A. andVági, S. Singular integrals in homogeneous spaces and some problems of classical analysis,Ann. Scuola Norm. Sup. Pisa,25 (1971), 575–648.
[22] Oleįnik, O. A. andRadkevič, E. V. Second order equations with nonnegative characteristics form, Amer. Math. Soc., Providence, (1973).
[23] Schwartz, L. Théorie des distributions, Hermann, Paris, (1966).
[24] Stein, E. M. Topics in harmonic analysis, Ann. of Math. Studies #63, Princeton University Press, Princeton, (1970). · Zbl 0193.10502
[25] Stein, E. M. Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, (1970). · Zbl 0207.13501
[26] Stein, E. M. Some problems in harmonic analysis suggested by symmetric spaces and semi-simple groups,Proc. Internat. Congress Math. Nice (1970), vol. I, 173–189.
[27] Stein, E. M. Singular integrals and estimates for the Cauchy-Riemann equations,Bull. Amer. Math. Soc.,79 (1973), 440–445. · Zbl 0257.35040
[28] Stein, E. M. andWeiss, G. Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, (1971).
[29] Trèves, F. Topological vector spaces, distributions, and kernels, Academic Press, New York, (1967). · Zbl 0171.10402
[30] Yosida, K. Functional analysis, 3rd ed.. Springer-Verlag, New York, (1971). · Zbl 0217.16001
[31] Zygmund, A. Trigonometric series, vol. II, Cambridge University Press, Cambridge, (1959). · Zbl 0085.05601
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.