Inequalities for functions regular in the unit circle
Published online by Cambridge University Press: 24 October 2008
Extract
Let f(z) = u(z) + iv(z) be a function regular for |z| < 1 with real and imaginary parts u(z) and u(z) respectively. The following theorems have been proved by Miss M. L. Cartwright(1) and (2).
Theorem A. if v(0) = 0, 0 < α < ∞ and
for 0 ≤ r < 1, 0 ≤ θ < 2π then
for 0 ≤ r < 1, 0 ≤ θ < 2π
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- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 1 , January 1962 , pp. 26 - 37
- Copyright
- Copyright © Cambridge Philosophical Society 1962
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