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Mathematische Annalen

, Volume 244, Issue 3, pp 243–262 | Cite as

Analysis on the Heisenberg group and estimates for functions in hardy classes of several complex variables

  • Steven G. Krantz
Article

Keywords

Complex Variable Heisenberg Group Hardy Classis 
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References

  1. 1.
    Coifman, R., Rochberg, R., Weiss, G.: Factorization theorems forH p spaces in several variables. Ann. Math.103, 611–635 (1976)Google Scholar
  2. 2.
    Coifman, R., Weiss, G.: Analyse Harmonique non-commutative sur certains espaces homogenes. Berlin, Heidelberg, New York: Springer 1970Google Scholar
  3. 3.
    Coifman, R., Weiss, G.: Extensions of Hardy spaces and their use in analysis. Bull. Am. Math. Soc.83, 569–645 (1977)Google Scholar
  4. 4.
    Fefferman, C., Stein, E.M.:H p spaces of several variables. Acta Math.129, 137–193 (1972)Google Scholar
  5. 5.
    Folland, G.B., Stein, E.M.: Estimates for the\(\bar \partial _b\) complex and analysis on the Heisenberg group. Commun. Pure Appl. Math.27, 429–522 (1974)Google Scholar
  6. 6.
    Garnett, J., Latter, R.: The atomic decomposition for Hardy spaces in several complex variables. Duke Math. J.45, 815–845 (1978)Google Scholar
  7. 7.
    Geller, D.: Fourier analysis on the Heisenberg group. Ph.D. Thesis, Princeton (1977)Google Scholar
  8. 8.
    Goldberg, D.: A local version of real Hardy spaces. Ph.D. Thesis, Princeton (1978)Google Scholar
  9. 9.
    Graham, I.: AnH p space theorem for the radial derivative of holomorphic functions on the unit ball inC n (preprint)Google Scholar
  10. 10.
    Hardy, G.H., Littlewood, J.E.: Some properties of fractional integrals. II. Math. Z.4, 403–439 (1932)Google Scholar
  11. 11.
    Hardy, G.H., Littlewood, J.E.: Theorems concerning mean values of analytic or harmonic functions. Q. J. Math. Oxford Ser.12, 221–256 (1941)Google Scholar
  12. 12.
    Krantz, S.: Minimal smoothness conditions on stratified nilpotent Lie groups. Trans. Am. Math. Soc. (to appear)Google Scholar
  13. 13.
    Latter, R.: The atomic decomposition of Hardy spaces. Ph.D. Thesis, UCLA (1977)Google Scholar
  14. 14.
    Latter, R.: A characterization ofH p(R n) in terms of atoms. Studia Math.62, 93–101 (1978)Google Scholar
  15. 15.
    Phong, D.H., Stein, E.M.: Estimates for the Bergman and Szego projections on strongly pseudoconvex domains. Duke Math. J.44, 695–704 (1977)Google Scholar
  16. 16.
    Rudin, W.: Holomorphic Lipschitz functions in balls. Comment. Math. Helv.53, 143–147 (1978)Google Scholar
  17. 17.
    Smith, K.T.: A generalization of an inequality of Hardy and Littlewood. Can. J. Math.8, 157–170 (1956)Google Scholar
  18. 18.
    Stein, E.M.: Boundary behavior of holomorphic functions of several complex variables. Princeton: Princeton University Press 1972Google Scholar
  19. 19.
    Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton: Princeton University Press 1970Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Steven G. Krantz
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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