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A characterization of $ H\sp 2$ classes on rank one symmetric spaces of noncompact type


Author: Patricio Cifuentes
Journal: Proc. Amer. Math. Soc. 106 (1989), 519-525
MSC: Primary 43A85; Secondary 22E30
DOI: https://doi.org/10.1090/S0002-9939-1989-0946631-7
MathSciNet review: 946631
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Abstract: A characterization of the Hardy class $ {H^2}$ on a rank one symmetric space of noncompact type by a Littlewood-Paley type operator defined through the Green potential of the norm square of the invariant gradient.


References [Enhancements On Off] (What's this?)

  • [1] P. Cifuentes, $ {H^p}$-classes on rank one symmetric spaces of noncompact type. I, Nontangential and probabilistic maximal functions, Trans. Amer. Math. Soc. 294 (1986), 133-149. MR 819939 (87h:43012a)
  • [2] -, $ {H^p}$-classes on rank one symmetric spaces of noncompact type. II, Nontangential maximal function and area integral, Bull. Sci. Math. 108 (1984), 355-371. MR 784673 (87h:43012b)
  • [3] R. Courant and D. Hilbert, Methods of mathematical Physics, vol. II, Interscience, New York, 1962. MR 0065391 (16:426a)
  • [4] A. Debiard, Espaces $ {H^p}$ au dessus de l'espace hermitien hyperbolique de $ {C^n}\left( {n > 1} \right)$, II, J. Funct. Anal. 40 (1981), 185-265. MR 609441 (82m:43016)
  • [5] R. K. Getoor and M. I. Sharpe, Conformal martingales, Invent. Math. 16 (1972), 271-308. MR 0305473 (46:4603)
  • [6] S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, New York, 1978. MR 514561 (80k:53081)
  • [7] -, Groups and geometric analysis, Academic Press, New York, 1984. MR 754767 (86c:22017)
  • [8] A. W. Knapp and R. E. Williamson, Poisson integrals and semisimple Lie groups, J. Analyse Math. 24 (1972), 53-76. MR 0308330 (46:7444)
  • [9] A. Korányi, Harmonic functions on symmetric spaces, Symmetric Spaces (W. Boothby and G. Weiss, eds.), Marcel Dekker, New York, 1972, 379-412. MR 0407541 (53:11314)
  • [10] P. A. Meyer, Le dual de $ {H^1}({{\mathbf{R}}^n})$ : démonstration probabiliste, Lecture Notes in Math. vol. 581, Springer-Verlag, Berlin, New York, 1977 pp. 132-195. MR 0651555 (58:31382)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0946631-7
Article copyright: © Copyright 1989 American Mathematical Society

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