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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 Jul;73(7):2174–2175. doi: 10.1073/pnas.73.7.2174

Maximal functions: Spherical means*

Elias M Stein 1
PMCID: PMC430482  PMID: 16592329

Abstract

Let [unk](f)(x) denote the supremum of the averages of f taken over all (surfaces of) spheres centered at x. Then f → [unk](f) is bounded on Lp(Rn), whenever p > n/(n - 1), and n ≥ 3.

Keywords: g-functions, almost-everywhere convergence, wave equation

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Selected References

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

  1. Nagel A., Riviere N., Wainger S. A maximal function associated to the curve (t, t). Proc Natl Acad Sci U S A. 1976 May;73(5):1416–1417. doi: 10.1073/pnas.73.5.1416. [DOI] [PMC free article] [PubMed] [Google Scholar]

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