HARDY-LITTLEWOOD PROPERTY WITH THE INNER LENGTH METRIC

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DOI QR Code

Kim, Ki-Won

  • 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.

키워드

Hardy-Littlewood property with the inner length netric;John disk;Lipschitz class

참고문헌

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피인용 문헌

  1. 1. Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces vol.2014, 2014, doi:10.4134/CKMS.2004.19.1.053