Journal of Mathematical Sciences

, Volume 134, Issue 4, pp 2288–2291

The Converse Fatou Theorem for Smooth Measures

  • E. S. Dubtsov
Article
  • 21 Downloads

Abstract

We prove the converse of the Fatou theorem for small Zygmund measures defined on the Euclidean space. Bibliography: 5 titles.

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REFERENCES

  1. 1.
    J. Brossard and L. Chevalier, “Probleme de Fatou ponctuel et derivabilite des mesures,” Acta Math., 164, 237–263 (1990).MathSciNetGoogle Scholar
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    J. J. Carmona and J. J. Donaire, “The converse of Fatou's theorem for Zygmund measures,” Pacific J. Math., 191, 207–222 (1999).MathSciNetGoogle Scholar
  3. 3.
    E. Doubtsov and A. Nicolau, “Symmetric and Zygmund measures in several variables,” Ann. Inst. Fourier (Grenoble), 52, 153–177 (2002).MathSciNetGoogle Scholar
  4. 4.
    L. H. Loomis, “The converse of the Fatou theorem for positive harmonic functions,” Trans. Amer. Math. Soc., 53, 239–250 (1943).MATHMathSciNetGoogle Scholar
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    W. Rudin, “Tauberian theorems for positive harmonic functions,” Nederl. Akad. Wetensch. Indag. Math., 40, 376–384 (1978).MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • E. S. Dubtsov
    • 1
  1. 1.St.Petersburg State UniversityRussia

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