The radial growth of univalent functions
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摘要
Let f(z) belong to the well-known class S of functions univalent in the unit disk. It is shown that, in a classical result of Spencer (Trans. Amer. Math. Soc. 48 (1940) 418), this lim-inf condition cannot be replaced by a lim-sup condition. There is a function f in S for which the set for which the lim-sup is positive is uncountably dense in every interval and its complement is of Baire Category I. Such a function cannot be close-to-convex.
论文关键词:Radial growth,Univalent functions,Uncountable sets
论文评审过程:Received 19 February 2003, Available online 21 March 2004.
论文官网地址:https://doi.org/10.1016/j.cam.2004.01.013