A characterization of $H^ 2$ classes on rank one symmetric spaces of noncompact type
HTML articles powered by AMS MathViewer
- by Patricio Cifuentes PDF
- Proc. Amer. Math. Soc. 106 (1989), 519-525 Request permission
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
- Patricio Cifuentes, $H^p$-classes on rank one symmetric spaces of noncompact type. I. Nontangential and probabilistic maximal functions, Trans. Amer. Math. Soc. 294 (1986), no. 1, 133–149. MR 819939, DOI 10.1090/S0002-9947-1986-0819939-5
- Patricio Cifuentes, $H^p$-classes on rank one symmetric spaces of noncompact type. I. Nontangential and probabilistic maximal functions, Trans. Amer. Math. Soc. 294 (1986), no. 1, 133–149. MR 819939, DOI 10.1090/S0002-9947-1986-0819939-5
- R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
- Amédée Debiard, Espaces $H^{p}$ au dessus de l’espace hermitien hyperbolique de $\textbf {C}^{n}$ $(n>1)$. II, J. Functional Analysis 40 (1981), no. 2, 185–265 (French, with English summary). MR 609441, DOI 10.1016/0022-1236(81)90067-7
- R. K. Getoor and M. J. Sharpe, Conformal martingales, Invent. Math. 16 (1972), 271–308. MR 305473, DOI 10.1007/BF01425714
- Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
- Sigurdur Helgason, Groups and geometric analysis, Pure and Applied Mathematics, vol. 113, Academic Press, Inc., Orlando, FL, 1984. Integral geometry, invariant differential operators, and spherical functions. MR 754767
- A. W. Knapp and R. E. Williamson, Poisson integrals and semisimple groups, J. Analyse Math. 24 (1971), 53–76. MR 308330, DOI 10.1007/BF02790369
- Adam Koranyi, Harmonic functions on symmetric spaces, Symmetric spaces (Short Courses, Washington Univ., St. Louis, Mo., 1969–1970), Pure and Appl. Math., Vol. 8, Dekker, New York, 1972, pp. 379–412. MR 0407541
- P. A. Meyer, Le dual de $H^{1}(\textbf {R}^{\nu })$: démonstrations probabilistes, Séminaire de Probabilités, XI (Univ. Strasbourg, Strasbourg, 1975/1976) Lecture Notes in Math., Vol. 581, Springer, Berlin, 1977, pp. 132–195 (French). MR 0651555
Additional Information
- © Copyright 1989 American Mathematical Society
- 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