Hardy-Littlewood property with the inner length metric
Commun. Korean Math. Soc. 2004 Vol. 19, No. 1, 53-62
Printed March 1, 2004
Kiwon Kim
Silla University
Abstract : A result of Hardy and Littlewood relates H\"older continuity of analytic functions in the unit disk with a bound on the derivative. Gehring and Martio extended this result to the class of uniform domains. We call it the Hardy-Littlewood property. Langmeyer further extended their result to the class of John disks in terms of the inner length metric. We call it the Hardy-Littlewood property with the inner length metric. In this paper we give several properties of a domain which satisfies the Hardy-Littlewood property with the inner length metric. Also we show some results on the Holder continuity of conjugate harmonic functions in various domains.
Keywords : Hardy-Littlewood property with the inner length metric, John disk, Lipschitz class
MSC numbers : 30C65, 30F45
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