Acta Mathematica

, Volume 155, Issue 1, pp 103–147 | Cite as

Balls and metrics defined by vector fields I: Basic properties

  • Alexander Nagel
  • Elias M. Stein
  • Stephen Wainger


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  1. [C]
    Carathéodory, C., Untersuchungen über die Grundlagen der Thermodynamik.Math. Ann., 67 (1909), 355–386.CrossRefMathSciNetGoogle Scholar
  2. [Ch]
    Chow, W. L., Über Systeme von linearen partiellen Differentialgleichungen erster Ordnung.Math. Ann., 117 (1940), 98–115.CrossRefGoogle Scholar
  3. [D]
    Dieudonné, J.,Foundations of modern analysis. Academic Press, New York, 1960.Google Scholar
  4. [FP]
    Fefferman, C. & Phong, D. H., Subelliptic eigenvalue problems, inConference on Harmonic Analysis in honor of Antoni Zygmund, vol. 2, pp. 590–606. Wadsworth, 1983.Google Scholar
  5. [FH]
    Folland, G. & Hung, H. T., Non-isotropic Lipschitz spaces, inHarmonic Analysis in Euclidean Spaces. Amer. Math. Soc., Part 2, pp. 391–394. Providence, 1979.Google Scholar
  6. [Ho]
    Hochschild, G.,The structure of Lie groups. Holden-Day Inc., San Francisco, London, Amsterdam, 1965.Google Scholar
  7. [H]
    Hörmander, L., Hypoelliptic second order differential equations.Acta Math., 119 (1967), 147–171.CrossRefMATHMathSciNetGoogle Scholar
  8. [NS]
    Nagel, A. &Stein, E. M.,Lectures on pseudo-differential operators. Math. Notes Series no. 24. Princeton Univ. Press, Princeton, 1979.Google Scholar
  9. [NSW]
    Nagel, A., Stein, E. M. &Wainger, S., Boundary behavior of functions holomorphic in domains of finite type.Proc. Nat. Acad. Sci. U.S.A., 78 (1981), 6596–6599.MathSciNetGoogle Scholar
  10. [RS]
    Rothschild, L. P. &Stein, E. M., Hypoelliptic differential operators and nilpotent groups.Acta Math., 137 (1976), 247–320.MathSciNetGoogle Scholar
  11. [Sa]
    Sanchez, A., Estimates for kernels associated to some subelliptic operators. Thesis, Princeton University, 1983.Google Scholar
  12. [St1]
    Stein, E. M.,Singular integrals and differentiability properties of functions. Princeton Univ. Press, Princeton, 1970.Google Scholar
  13. [St2]
    —,Boundary behavior of holomorphic functions of several complex variables. Math. Notes Series no. 11. Princeton Univ. Press, Princeton, 1972.Google Scholar

Copyright information

© Almqvist & Wiksell 1985

Authors and Affiliations

  • Alexander Nagel
    • 1
  • Elias M. Stein
    • 2
  • Stephen Wainger
    • 3
  1. 1.University of WisconsinMadisonUSA
  2. 2.Princeton UniversityPrincetonUSA
  3. 3.University of WisconsinMadisonUSA

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