Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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HARDY-LITTLEWOOD PROPERTY AND α-QUASIHYPERBOLIC METRIC

  • Kim, Ki Won (Department of Mathematics Education College of Education Silla University) ;
  • Ryu, Jeong Seog (Department of Mathematics Education College of Education Hongik University)
  • Received : 2018.12.10
  • Accepted : 2019.03.15
  • Published : 2020.01.31
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Abstract

Hardy and Littlewood found a relation between the smoothness of the radial limit of an analytic function on the unit disk D ⊂ ℂ and the growth of its derivative. It is reasonable to expect an analytic function to be smooth on the boundary if its derivative grows slowly, and conversely. Gehring and Martio showed this principle for uniform domains in ℝ2. Astala and Gehring proved quasiconformal analogue of this principle for uniform domains in ℝn. We consider α-quasihyperbolic metric, kαD and we extend it to proper domains in ℝn.

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References

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