Keywords
- Harmonic Function
- Conformal Mapping
- Subharmonic Function
- Lebesgue Dominate Convergence Theorem
- Positive Harmonic Function
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References
J.M. Anderson, J.G. Clunie, and Ch. Pommerenke, On Bloch functions and normal functions, J. Reine Angew. Math., 270 (1974), 12–37.
F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A., 41 (1955), 379–382.
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.
B. Hanson, The zero distribution of holomorphic functions in the unit disc, Proc. London Math. Soc. (3), 51 (1985), 339–368.
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.
W.K. Hayman and B. Korenblum, A critical growth rate for functions regular in the disk, Michigan Math. J., 27 (1980), 21–30.
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.
B. Korenblum, An extension of the Nevanlinna theory, Acta Math., 135 (1975), 187–219.
B. Korenblum, A Beurling-type theorem, Acta Math., 138 (1977), 263–291.
B. Korenblum, Some problems in potential theory and the notion of harmonic entropy, Bull. A.M.S., 8 (1983), 459–462.
B. Korenblum, P.J. Rippon, and K. Samotij, On integrals of harmonic functions over annuli, preprint.
C.N. Linden, Functions regular in the unit circle, Proc. Cambridge Philos. Soc., 52 (1956), 49–60.
C.N. Linden, Regular functions of restricted growth and their zeros in tangential regions, Trans. A.M.S., 275 (1983), 679–686.
Ch. Pommerenke, On the growth of normal analytic functions, J. Analyse Math., 36 (1979), 227–232.
F. Riesz, Sur certains systèmes singuliers d'équations intégrals, Ann. Sci. de l'Ecole Normale Sup. Ser. 3, 28 (1911), 33–62.
P.J. Rippon, A boundary estimate for harmonic functions, Math. Proc. Camb. Phil. Soc., 91 (1982), 79–90.
P.J. Rippon, The fine boundary behavior of certain delta-subharmonic functions, J. London Math. Soc., (2), 26 (1982), 487–503.
P.J. Rippon, Ambiguous points of functions in the unit ball of euclidean space, Bull. London Math. Soc., 15 (1983), 336–338.
K. Samotij, A representation theorem for harmonic functions in the ball in ℝn, Ann. Acad. Sci. Fenn. Ser. A.I. Math., to appear.
K. Samotij, A critical growth rate for harmonic and subharmonic functions, Colloq. Math., to appear.
A.A. Shaginyan, A boundary singularity of functions that are harmonic in a ball, Akad. Nauk Armyan. SSSr Dokl., 78 (1984), 51–52.
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.
S.E. Warschawski, On boundary derivatives in conformal mapping, Ann. Acad. Sci. Fenn. Ser. A.I. Math., 420 (1968).
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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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