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Some Remarks on Angular Derivatives and Julia's Lemma
Published online by Cambridge University Press: 20 November 2018
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Let w = f(z) be holomorphic on the unit disk D = { z: | z | < 1}, with the additional restrictions that | f ( z ) | < l and , where
denotes the (outer) angular limit of f (z) at z = 1. Let us now define
and then focus our attention on the behaviour of g(z) in an arbitrary angular neighbourhood of z = 1. Whenever
exists, this limit is commonly referred to as the angular derivative of f(z) at z = 1.
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- Copyright © Canadian Mathematical Society 1966
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