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The generalized Ahlfors-Heins theorem in R3

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Part of the Lecture Notes in Mathematics book series (LNM,volume 419)

Keywords

  • Fine Limit
  • Subharmonic Function
  • Superharmonic Function
  • Fine Topology
  • Convolution Inequality

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References

  1. Doob, J. L.: A non-probabilistic proof of the relative Fatou theorem.-Ann. Inst. Fourier (Grenoble) 9, 1959, pp.293–300.

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  2. Essén, M.: A generalization of the Ahlfors-Heins theorem.-Bull. Amer. Math. Soc. 75, 1969, pp.127–131.

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  3. -"-: A generalization of the Ahlfors-Heins theorem.-Trans. Amer. Math. Soc. 142, 1969, pp.331–344.

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  4. Helms, L. L.: Introduction to potential theory.-Pure and applied mathematics 22. Wiley-Interscience, a Division of John Wiley & Sons, New York / London / Sydney / Toronto, 1969.

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  5. Keller, H.: Über das Anwachsen von Potentialfunktionen im dreidimensionalen Raum.-Ann. Acad. Sci. Fenn. A.I.83, 1950.

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  6. Lelong, Jacqueline: Propriétés des fonctions surharmoniques positives dans un demi-espace.-C. R. Acad. Sci. Paris 226, 1948, pp.1161–1163.

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  7. Lelong-Ferrand, Jacqueline: Étude des fonctions surharmoniques positives dans un cylindre ou dans un cône.-C. R. Acad. Sci. Paris 229, 1949, pp.340–341.

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  8. Lelong-Ferrand, Jacqueline: Extension du théorème de Phràgmén-Lindelöf-Heins aux fonctions sous-harmoniques dans un cône ou dans un cylindre.-C. R. Acad. Sci. Paris 229, 1949, pp.411–413.

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  9. Lewis, J. L.: Subharmonic functions in certain regions.-Trans. Amer. Math. Soc. 167, 1972, pp.191–201.

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  10. -"-A note on Essén's generalization of the Ahlfors-Heins theorem.-Trans. Amer. Math. Soc. (to appear).

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© 1974 Springer-Verlag

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Essén, M. (1974). The generalized Ahlfors-Heins theorem in R3 . In: Lehto, O., Louhivaara, I.S., Nevanlinna, R. (eds) Topics in Analysis. Lecture Notes in Mathematics, vol 419. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064715

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  • DOI: https://doi.org/10.1007/BFb0064715

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06965-2

  • Online ISBN: 978-3-540-37907-2

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