𝐻^{𝑝}-classes on rank one symmetric spaces of noncompact type. I. Nontangential and probabilistic maximal functions

Cifuentes, Patricio

doi:10.1090/S0002-9947-1986-0819939-5

$H^ p$-classes on rank one symmetric spaces of noncompact type. I. Nontangential and probabilistic maximal functions
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Trans. Amer. Math. Soc. 294 (1986), 133-149 Request permission

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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