Tangential asymptotic values of bounded analytic functions
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- by U. V. Satyanarayana and Max L. Weiss PDF
- Proc. Amer. Math. Soc. 41 (1973), 167-172 Request permission
Abstract:
Suppose $f$ is a bounded analytic function on the unit disc whose Fatou boundary function is approximately continuous from above at 1 with value 0. It is well known that $f$ tends to zero radially and therefore along every nontangential arc. Tanaka [3] and Boehme and Weiss [1] have shown that $f$ must also tend to zero along certain arcs which are tangential from above. The purpose of this paper is to improve their results by producing a larger collection of such tangential arcs along which $f$ tends to zero. We construct a class of examples to show that our result is actually better.References
- T. K. Boehme and Max L. Weiss, Extensions of Fatou’s theorem to tangential asymptotic values, Proc. Amer. Math. Soc. 27 (1971), 289–298. MR 273039, DOI 10.1090/S0002-9939-1971-0273039-9
- U. V. Satyanarayana and Max L. Weiss, The geometry of convex curves tending to $1$ in the unit disc, Proc. Amer. Math. Soc. 41 (1973), 159–166. MR 318497, DOI 10.1090/S0002-9939-1973-0318497-8
- Chuji Tanaka, On the metric cluster values of the bounded regular function in the unit disk, Mem. School Sci. Engrg. Waseda Univ. 31 (1967), 119–129. MR 247101
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 41 (1973), 167-172
- MSC: Primary 30A78
- DOI: https://doi.org/10.1090/S0002-9939-1973-0318498-X
- MathSciNet review: 0318498