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The higher derivations of functions bounded in various senses
Published online by Cambridge University Press: 17 April 2009
Abstract
An extension (Theorem 1) of Schwarz and Pick's lemma motivates us to study the analogues for functions which are bounded in the sense of Bloch, normal, or yoshida. A typical result is that, for a function f holomorphic in D = {|z| < 1} and Bloch, that is, , with the expansion f(w) = c0 + cn (w − z)n + … (n ≧ 1) about 2 ε D, we have (1 − |z|2)n|f(n) (z)|/n! ≦ Anα, where An is an absclute constant; the estimate is sharp.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 34 , Issue 3 , December 1986 , pp. 321 - 334
- Copyright
- Copyright © Australian Mathematical Society 1986
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