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The arc-length variation of analytic capacity and a conformal geometry

Published online by Cambridge University Press:  22 January 2016

Takafumi Murai
Takafumi Murai*
Affiliation:
Department of Mathematics School of Science Nagoya University, Chikusa-ku, Nagoya, 464-01, Japan
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For a domain Ω in the extended complex plane C ∪{∞}, H∞(Ω) denotes the Banach space of bounded analytic functions in Ω with supremum norm ∥ · ∥H∞ For ζ ∈ Ω, we put

where f′(∞) = lim,z→∞z{f (∞) = f(z)} if ζ = ∞.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 125 , March 1992 , pp. 151 - 216
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

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