A curvilinear extension of Iversen-Tsuji’s theorem for simply connected domain

Choi, Un Haing

doi:10.1090/S0002-9939-1977-0447576-3

A curvilinear extension of Iversen-Tsuji’s theorem for simply connected domain
HTML articles powered by AMS MathViewer

by Un Haing Choi PDF

Proc. Amer. Math. Soc. 64 (1977), 47-51 Request permission

Abstract:

Let D be a simply connected domain with at least two boundary points in the complex plane, and t a boundary point of D. For a meromorphic function $f(z)$ in D, $\lim \sup |f(z)|{\text {as}}\;z \to t$ is given in terms of accessible boundary points and prime ends. This gives a curvilinear extension of Iversen-Tsuji’s Theorem for a simply connected domain.

References

Kiyoshi Noshiro, Cluster sets, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Heft 28, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1960. MR 0133464, DOI 10.1007/978-3-642-85928-1
E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999, DOI 10.1017/CBO9780511566134
F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 379–382. MR 69888, DOI 10.1073/pnas.41.6.379
Kikuji Matsumoto, On some boundary problems in the theory of conformal mappings of Jordan domains, Nagoya Math. J. 24 (1964), 129–141. MR 200430, DOI 10.1017/S0027763000011363
Frederick Bagemihl, A curvilinear extension of the maximum modulus principle, Proc. Nat. Acad. Sci. U.S.A. 63 (1969), 36–37. MR 262494, DOI 10.1073/pnas.63.1.36