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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Extremal properties of Green functions and A. Weitsman's conjecture


Author: Alexander Fryntov
Journal: Trans. Amer. Math. Soc. 345 (1994), 511-525
MSC: Primary 31A05
MathSciNet review: 1181183
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Abstract: A new version of the symmetrization theorem is proved. Using a modification of the $ \ast $-function of Baernstein we construct an operator which maps a family of $ \delta $-subharmonic functions defined on an annulus into a family of subharmonic functions on an annular sector. Applying this operator to the Green function of special domains we prove A. Weitsman's conjecture linked with exact estimates of the Green functions of these domains.


References [Enhancements On Off] (What's this?)

  • [1] Albert Baernstein II, Integral means, univalent functions and circular symmetrization, Acta Math. 133 (1974), 139–169. MR 0417406 (54 #5456)
  • [2] Albert Baernstein II, An extremal problem for certain subharmonic functions in the plane, Rev. Mat. Iberoamericana 4 (1988), no. 2, 199–218. MR 1028739 (90k:31001), http://dx.doi.org/10.4171/RMI/71
  • [3] A. E. Fryntov, An extremal problem of potential theory, Dokl. Akad. Nauk SSSR 300 (1988), no. 4, 819–820 (Russian); English transl., Soviet Math. Dokl. 37 (1988), no. 3, 754–755. MR 950785
  • [4] W. K. Hayman and P. B. Kennedy, Subharmonic functions, Academic Press, San Diego, 1976.
  • [5] A. Weitsman, Some remarks on the spread of a Nevanlinna deficiency, Mittag-Leffler Technical report No. 7, 1977.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1181183-7
PII: S 0002-9947(1994)1181183-7
Keywords: Subharmonic function, Green function, symmetrization
Article copyright: © Copyright 1994 American Mathematical Society