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Subharmonic functions with unilateral growth conditions

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1275)

Keywords

  • Harmonic Function
  • Conformal Mapping
  • Subharmonic Function
  • Lebesgue Dominate Convergence Theorem
  • Positive Harmonic Function

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References

  1. J.M. Anderson, J.G. Clunie, and Ch. Pommerenke, On Bloch functions and normal functions, J. Reine Angew. Math., 270 (1974), 12–37.

    MathSciNet  MATH  Google Scholar 

  2. F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A., 41 (1955), 379–382.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. J.G. Clunie and P.J. Rippon, On harmonic functions with integrable maximum modulus, Ann. Acad. Sci. Fenn., Ser. A.I. Math., 8 (1983), 333–342.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. B. Hanson, The zero distribution of holomorphic functions in the unit disc, Proc. London Math. Soc. (3), 51 (1985), 339–368.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. W.K. Hayman and B. Korenblum, An extension of the Riesz-Herglotz formula, Ann. Acad. Sci. Fenn. Ser. A.I. Math., 2 (1976), 175–201.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. W.K. Hayman and B. Korenblum, A critical growth rate for functions regular in the disk, Michigan Math. J., 27 (1980), 21–30.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. G. Herglotz, Ueber Potenzreihen mit positivem, reelem Teil in Einheitskreise, Ber. ü Verh. der Kgl sächs Ges. der Wissen. zu zu Leipzig, Math. Phys. Kl. 63 (1911), 501–511.

    Google Scholar 

  8. B. Korenblum, An extension of the Nevanlinna theory, Acta Math., 135 (1975), 187–219.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. B. Korenblum, A Beurling-type theorem, Acta Math., 138 (1977), 263–291.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. B. Korenblum, Some problems in potential theory and the notion of harmonic entropy, Bull. A.M.S., 8 (1983), 459–462.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. B. Korenblum, P.J. Rippon, and K. Samotij, On integrals of harmonic functions over annuli, preprint.

    Google Scholar 

  12. C.N. Linden, Functions regular in the unit circle, Proc. Cambridge Philos. Soc., 52 (1956), 49–60.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. C.N. Linden, Regular functions of restricted growth and their zeros in tangential regions, Trans. A.M.S., 275 (1983), 679–686.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Ch. Pommerenke, On the growth of normal analytic functions, J. Analyse Math., 36 (1979), 227–232.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. F. Riesz, Sur certains systèmes singuliers d'équations intégrals, Ann. Sci. de l'Ecole Normale Sup. Ser. 3, 28 (1911), 33–62.

    MathSciNet  MATH  Google Scholar 

  16. P.J. Rippon, A boundary estimate for harmonic functions, Math. Proc. Camb. Phil. Soc., 91 (1982), 79–90.

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. P.J. Rippon, The fine boundary behavior of certain delta-subharmonic functions, J. London Math. Soc., (2), 26 (1982), 487–503.

    CrossRef  MathSciNet  MATH  Google Scholar 

  18. P.J. Rippon, Ambiguous points of functions in the unit ball of euclidean space, Bull. London Math. Soc., 15 (1983), 336–338.

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. K. Samotij, A representation theorem for harmonic functions in the ball in ℝn, Ann. Acad. Sci. Fenn. Ser. A.I. Math., to appear.

    Google Scholar 

  20. K. Samotij, A critical growth rate for harmonic and subharmonic functions, Colloq. Math., to appear.

    Google Scholar 

  21. A.A. Shaginyan, A boundary singularity of functions that are harmonic in a ball, Akad. Nauk Armyan. SSSr Dokl., 78 (1984), 51–52.

    MathSciNet  MATH  Google Scholar 

  22. H.S. Shapiro and A.L. Shields, On the zeros of functions with finite Dirichlet integral and some related function spaces, Math. Zeit., 80 (1962), 217–229.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. S.E. Warschawski, On boundary derivatives in conformal mapping, Ann. Acad. Sci. Fenn. Ser. A.I. Math., 420 (1968).

    Google Scholar 

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Dedicated to Professor Maurice Heins on the occasion of his 70th birthday

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© 1987 Springer-Verlag

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Rippon, P.J. (1987). Subharmonic functions with unilateral growth conditions. In: Berenstein, C.A. (eds) Complex Analysis I. Lecture Notes in Mathematics, vol 1275. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078357

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  • DOI: https://doi.org/10.1007/BFb0078357

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18356-3

  • Online ISBN: 978-3-540-47899-7

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