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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ H\sp p$-classes on rank one symmetric spaces of noncompact type. I. Nontangential and probabilistic maximal functions


Author: Patricio Cifuentes
Journal: Trans. Amer. Math. Soc. 294 (1986), 133-149
MSC: Primary 43A85; Secondary 22E30, 32A35, 58G32, 60J65
MathSciNet review: 819939
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Abstract: Two kinds of $ {H^p}$-classes of harmonic functions are defined on a general rank one symmetric space of noncompact type. The first one is introduced by using a nontangential maximal function. The second is related to the diffusion generated by the Laplace-Beltrami operator. The equivalence of the two classes is proven for $ 0 < p < \infty $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0819939-5
PII: S 0002-9947(1986)0819939-5
Keywords: $ {H^p}$-classes, harmonic functions, rank one symmetric spaces, diffusion
Article copyright: © Copyright 1986 American Mathematical Society