대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제19권1호
  • /
  • Pages.53-62
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  • 2004
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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HARDY-LITTLEWOOD PROPERTY WITH THE INNER LENGTH METRIC

  • Kim, Ki-Won (Department of Mathematics Silla University)
  • 발행 : 2004.01.01
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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
  2. Math. Scand. v.65 Auasihyperbolic geodesics in John domains F.W.Gehring;K.Hang;O.Martio https://doi.org/10.7146/math.scand.a-12267
  3. Complex Variables Theory Appl. v.2 Auasidisks and the Hardy-Littlewood property F.W.Gehring;O.Martio https://doi.org/10.1080/17476938308814032
  4. Ann. Acad. Sci. Fenn. Math. v.10 Lipschitz Classes and quasiconformal mappings F.W.Gehring https://doi.org/10.5186/aasfm.1985.1022
  5. Math. Z. v.34 Some properties of fractional intergrals. Ⅱ G.H.Hardy;J.E.Littlewood https://doi.org/10.1007/BF01180596
  6. Math. Scand. v.83 Hormonic measure and hyperbolic distance in John disks K.Kim;N.Langmeyer https://doi.org/10.7146/math.scand.a-13857
  7. Comples Variavles Theory Appl. v.4 Distances and the Hardy-Littlewood property R.Kaufman;J.M.Wu https://doi.org/10.1080/17476938408814086
  8. Ann. Acad. Sci. Fenn. Math. v.23 The quasihyperbolic metric, growth and John domains N.Langmeyer
  9. Ann. Acad. Sci. Fenn. Math. Diss. v.56 Lipα-extension domains V.Lappalanien
  10. Esposition. Math. v.9 John disks R.Nakki;J.Valsala

피인용 문헌

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