On Carleson’s Uniqueness Theorem for Analytic Functions with a Finite Dirichlet Integral

  • V. G. Maz’ya
  • V. P. Khavin
Part of the Problems in Mathematical Analysis / Problemy Matematicheskogo Analiza / Πроблемы Математического Анализа book series (PMA)


The present article contains the formulation of a theorem which supplements the well-known uniqueness theorem for analytic functions with a finite Dirichlet integral established by L. Carleson [1].


Unit Circle Satisfying Condition Potential Theory Uniqueness Theorem Borel Measure 
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Literature Cited

  1. 1.
    L. Carleson, “Sets of uniqueness for functions regular in the unit circle,” Acta Mathematica, Vol. 87, Nos. 3–4, pp. 325–345 (1952).MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    J. P. Kahane and R. Salem, Ensembles Parfaits et Séries Trigonométriques, Paris (1966).Google Scholar
  3. 3.
    N. S. Landkof, Fundamentals of Modern Potential Theory [in Russian], GITTL, Moscow (1966).Google Scholar
  4. 4.
    J. Deny and J. L. Lions, “Les espaces du type de Beppo Levi,” Annales de l’Institut Fourier, Vol. 5, pp. 305–370 (1953).MathSciNetCrossRefGoogle Scholar

Copyright information

© Consultants Bureau, New York 1971

Authors and Affiliations

  • V. G. Maz’ya
  • V. P. Khavin

There are no affiliations available

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