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Subelliptic estimates and function spaces on nilpotent Lie groups

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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.

    MATH  MathSciNet  Google Scholar 

  2. Calderón, A. P., Lebesgue spaces of differentiable functions and distributions,Proc. Symp. Pure Math.,4 (1961), 33–49.

    Google Scholar 

  3. Coifman, R. andWeiss, G.Analyse harmonique non-commutative sur certains espaces homogènes, Lecture notes #242, Springer-Verlag, Berlin, (1971).

    MATH  Google Scholar 

  4. Dyer, J. L. A nilpotent Lie algebra with nilpotent automorphism group,Bull. Amer. Math. Soc.,76 (1970), 52–56.

    Article  MATH  MathSciNet  Google Scholar 

  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).

    MATH  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  8. Guillemin, V. andSternberg, S. Subelliptic estimates for complexes,Proc. Nat. Acad. Sci. U.S.A.,67 (1970), 271–274.

    Article  MATH  MathSciNet  Google Scholar 

  9. Hochschild, G.The structure of Lie groups, Holden-Day, San Francisco, (1965).

    MATH  Google Scholar 

  10. Hörmander, L. Hypoelliptic second-order differential equations,Acta Math.,119 (1967), 147–171.

    Article  MATH  MathSciNet  Google Scholar 

  11. Hunt, G. A. Semigroups of measures on Lie groups,Trans. Amer. Math. Soc.,81 (1956), 264–293.

    Article  MATH  MathSciNet  Google Scholar 

  12. Jørgensen, P. Representations of differential operators on a Lie group, to appear.

  13. Knapp, A. W. andStein, E. M. Intertwining operators for semi-simple groups,Ann. of Math.,93 (1971), 489–578.

    Article  MathSciNet  Google Scholar 

  14. Kohn, J. J. andNirenberg, L. Non-coercive boundary value problems,Comm. Pure Appl. Math.,18 (1965), 443–492.

    Article  MATH  MathSciNet  Google Scholar 

  15. Komatsu, H. Fractional powers of operators,Pac. J. Math.,19 (1966), 285–346.

    MATH  MathSciNet  Google Scholar 

  16. Komatsu, H. Fractional powers of operators, II: Interpolation spaces,Pac. J. Math.,21 (1967), 89–111.

    MATH  MathSciNet  Google Scholar 

  17. Komatsu, H. Fractional powers of operators, III: Negative powers,J. Math. Soc. Japan,21 (1969), 205–220.

    Article  MathSciNet  Google Scholar 

  18. Komatsu, H. Fractional powers of operators, IV: Potential operators,J. Math. Soc. Japan,21 (1969), 221–228.

    MathSciNet  Google Scholar 

  19. Komatsu, H. Fractional powers of operators, V: Dual operators,J. Fac. Sci. Univ. Tokyo, Sec. IA,17 (1970), 373–396.

    MATH  MathSciNet  Google Scholar 

  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.

    MATH  MathSciNet  Google Scholar 

  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.

    MathSciNet  Google Scholar 

  22. Oleįnik, O. A. andRadkevič, E. V.Second order equations with nonnegative characteristics form, Amer. Math. Soc., Providence, (1973).

    Google Scholar 

  23. Schwartz, L.Théorie des distributions, Hermann, Paris, (1966).

    MATH  Google Scholar 

  24. Stein, E. M.Topics in harmonic analysis, Ann. of Math. Studies #63, Princeton University Press, Princeton, (1970).

    MATH  Google Scholar 

  25. Stein, E. M.Singular integrals and differentiability properties of functions, Princeton University Press, Princeton, (1970).

    MATH  Google Scholar 

  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.

    Google Scholar 

  27. Stein, E. M. Singular integrals and estimates for the Cauchy-Riemann equations,Bull. Amer. Math. Soc.,79 (1973), 440–445.

    Article  MATH  MathSciNet  Google Scholar 

  28. Stein, E. M. andWeiss, G.Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, (1971).

    MATH  Google Scholar 

  29. Trèves, F.Topological vector spaces, distributions, and kernels, Academic Press, New York, (1967).

    MATH  Google Scholar 

  30. Yosida, K.Functional analysis, 3rd ed.. Springer-Verlag, New York, (1971).

    MATH  Google Scholar 

  31. Zygmund, A.Trigonometric series, vol. II, Cambridge University Press, Cambridge, (1959).

    Google Scholar 

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Research partially supported by National Science Foundation Grant GP-38220.

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Folland, G.B. Subelliptic estimates and function spaces on nilpotent Lie groups. Ark. Mat. 13, 161–207 (1975). https://doi.org/10.1007/BF02386204

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