Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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HARDY-LITTLEWOOD PROPERTY WITH THE INNER LENGTH METRIC

  • Kim, Ki-Won (Department of Mathematics Silla University)
  • Published : 2004.01.01
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Abstract

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. 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.

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References

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