Subharmonic versions of Fatou’s theorem
HTML articles powered by AMS MathViewer
- by James L. Meek PDF
- Proc. Amer. Math. Soc. 30 (1971), 313-317 Request permission
Abstract:
A theorem of Fatou concerning the boundary behavior of bounded harmonic functions in the unit disk is extended to normal subharmonic functions. A question—which has been answered in the normal holomorphic and normal harmonic cases—concerning existence of Fatou points for normal subharmonic functions is posed.References
- Maynard G. Arsove, The Lusin-Privalov theorem for subharmonic functions, Proc. London Math. Soc. (3) 14 (1964), 260–270. MR 160927, DOI 10.1112/plms/s3-14.2.260
- F. Bagemihl and W. Seidel, Koebe arcs and Fatou points of normal functions, Comment. Math. Helv. 36 (1961), 9–18. MR 141786, DOI 10.1007/BF02566888
- C. Carathéodory, Conformal representation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 28, Cambridge, at the University Press, 1952. 2d ed. MR 0046435
- Peter A. Lappan, Fatou points of harmonic normal functions and uniformly normal functions, Math. Z. 102 (1967), 110–114. MR 222265, DOI 10.1007/BF01112077
- Olli Lehto and K. I. Virtanen, Boundary behaviour and normal meromorphic functions, Acta Math. 97 (1957), 47–65. MR 87746, DOI 10.1007/BF02392392 J. E. Littlewood, On functions subharmonic in a circle. II, Proc. London Math. Soc. (2) 28 (1928), 383-394.
- D. C. Rung, Asymptotic values of normal subharmonic functions, Math. Z. 84 (1964), 9–15. MR 179374, DOI 10.1007/BF01112205
- Elmer Tolsted, Limiting values of subharmonic functions, Proc. Amer. Math. Soc. 1 (1950), 636–647. MR 39862, DOI 10.1090/S0002-9939-1950-0039862-7
- M. Tsuji, Potential theory in modern function theory, Maruzen Co. Ltd., Tokyo, 1959. MR 0114894
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 313-317
- MSC: Primary 31.15; Secondary 30.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280728-9
- MathSciNet review: 0280728