• 대한수학회보
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• 제43권2호
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• pp.395-410
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• 2006

We characterize the class of uniformly John domains in terms of the quasihyperbolic metric and from the result we get some analogues of the Hardy-Littlewood property for ${\alpha} = 0$ in uniformly John domains.

• East Asian mathematical journal
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• 제19권2호
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• pp.291-303
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• 2003

A result of Hardy and Littlewood relates Holder 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. In this paper we obtain a similar result to the class of uniformly John domains in terms of the inner diameter metric. We give several properties of a domain with the property. Also we show some results on the Holder continuity of conjugate harmonic functions in the above domains.