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HARDY-LITTLEWOOD PROPERTY WITH THE INNER LENGTH METRIC

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

초록

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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참고문헌

  1. Monatsh. Math. v.115 Lipschitz Classes and the Hardy Littlewood Property K.Astala;K.Hag;P.Hag;V.Lapalainen https://doi.org/10.1007/BF01667307
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  3. Complex Variables Theory Appl. v.2 Auasidisks and the Hardy-Littlewood property F.W.Gehring;O.Martio https://doi.org/10.1080/17476938308814032
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피인용 문헌

  1. Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces vol.2014, 2014, https://doi.org/10.1155/2014/895074