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The higher derivations of functions bounded in various senses

Published online by Cambridge University Press:  17 April 2009

Shinji Yamashita
Shinji Yamashita
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Fukasawa, Setagaya, Tokyo 158, Japan
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Abstract

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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

References

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