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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1976 Aug;73(8):2547–2549. doi: 10.1073/pnas.73.8.2547

Maximal functions: Poisson integrals on symmetric spaces*

Elias M Stein 1
PMCID: PMC430684  PMID: 16592338

Abstract

Let u be a harmonic function on a symmetric space which is the Poisson integral of a function f in Lp, 1 ≤ p ≤ ∞. Then u converges restrictedly and admissibly to f almost everywhere. This result is proved by obtaining an appropriate maximal theorem which takes into account the structure of the Poisson kernel.

Keywords: harmonic functions, restricted and admissible convergence

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Stein E. M. Maximal functions: Homogeneous curves. Proc Natl Acad Sci U S A. 1976 Jul;73(7):2176–2177. doi: 10.1073/pnas.73.7.2176. [DOI] [PMC free article] [PubMed] [Google Scholar]

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