• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.11-24
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• 2012

We characterize the class of inner uniform domains in terms of the quasihyperbolic metric and the quasihyperbolic geodesic. We also characterize uniform domains and inner uniform domains in terms of weak Bloch functions.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.395-410
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• 2006

We characterize the class of uniformly John domains in terms of the quasihyperbolic metric and from the result we get some analogues of the Hardy-Littlewood property for ${\alpha} = 0$ in uniformly John domains.

• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.243-250
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• 2020

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, k^α_D and we extend it to proper domains in ℝⁿ.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.423-435
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• 2012

We give some properties of weak Bloch functions and also give some properties of ${\phi}$-uniform domains and ${\phi}$-John domains in terms of moduli of continuity of Bloch functions and weak Bloch functions.