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Transactions of the American Mathematical Society

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Comparison between analytic capacity and the Buffon needle probability


Author: Takafumi Murai
Journal: Trans. Amer. Math. Soc. 304 (1987), 501-514
MSC: Primary 30C85; Secondary 28A12
MathSciNet review: 911082
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Abstract: We show that analytic capacity and the Buffon needle probability are not comparable.


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  • [1] Alexander M. Davie and Bernt Øksendal, Analytic capacity and differentiability properties of finely harmonic functions, Acta Math. 149 (1982), no. 1-2, 127–152. MR 674169, 10.1007/BF02392352
  • [2] G. David, A lower estimate for the norm of the Cauchy integral operator on Lipschitz curves, preprint.
  • [3] John Garnett, Analytic capacity and measure, Lecture Notes in Mathematics, Vol. 297, Springer-Verlag, Berlin-New York, 1972. MR 0454006
  • [4] L. D. Ivanov, On sets of analytic capacity zero, Lecture Notes in Math., vol. 1043, Springer-Verlag, 1984, pp. 498-501.
  • [5] J. L. Journé, Calderón-Zygmund operators, pseudo-differential operators and the Cauchy integral of Calderón, Lecture Notes in Math., vol. 994, Springer-Verlag, 1983.
  • [6] D. E. Marshall, Removable sets for bounded analytic functions, Lecture Notes in Math., vol. 1043, Springer-Verlag, 1984, pp. 485-490.
  • [7] Takafumi Murai, Boundedness of singular integral operators of Calderón type. VI, Nagoya Math. J. 102 (1986), 127–133. MR 846134
  • [8] L. A. Santaló, Introduction to integral geometry, Actualités Sci. Ind., no. 1198, Publ. Inst. Math. Univ. Nancago II. Herman et Cie, Paris, 1953. MR 0060840

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0911082-0
Keywords: Analytic capacity, the Buffon needle probability
Article copyright: © Copyright 1987 American Mathematical Society