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Length and area inequalities for the derivative of a bounded and holomorphic function
Published online by Cambridge University Press: 17 April 2009
Abstract
The Schwarz-Pick lemma,
for f analytic and bounded, |f|<1, in the disk |z|<1, is refined:
where Φ(z, r) is a quantity determined by the non-Euclidean area of the image of
and ψ(z, r) is that determined by the non-Euclidean length of the image of the boundary of D(z, r). The multiplicities in both images by f are not counted.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 30 , Issue 3 , December 1984 , pp. 457 - 462
- Copyright
- Copyright © Australian Mathematical Society 1984
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