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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Poisson integrals and nontangential limits
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by Victor L. Shapiro PDF
Proc. Amer. Math. Soc. 134 (2006), 3181-3189 Request permission


A new result is established for nontangential limits of the Poisson integral of an $f\in L^{p}(\mathbf {R}^{N})$ for $N\geq 2.$ This is accomplished by showing for $N=2,\exists f$ such that the $\sigma$-set of $f$ strictly contains the Lebesgue set of $f.$ A similar theorem is also proved for Gauss-Weierstrass integrals, giving a new result for solutions of the heat equation.
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Additional Information
  • Victor L. Shapiro
  • Affiliation: Department of Mathematics, University of California, Riverside, California 92521
  • Email:
  • Received by editor(s): September 24, 2004
  • Received by editor(s) in revised form: April 26, 2005
  • Published electronically: June 1, 2006
  • Communicated by: Juha M. Heinonen
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3181-3189
  • MSC (2000): Primary 31B25, 35K20; Secondary 35J05, 35K05
  • DOI:
  • MathSciNet review: 2231901