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Vietnam Journal of Mathematics 36:1(2008) 71-78

Quasiconformal Analogues of the Hardy-Littlewood Property in Uniformly John Domains

Xiaohui Zhang, Gendi Wang, and Yuming Chu

Abstract.  A result of Hardy-Littlewood relates Hölder continuity of analytic functions over the unit disk to the growth of the derivative. Astala and Gehring extend this result to a quasiconformal analogue in uniform domain in n-dimensional space. In this paper, we prove some quasiconformal analogues of Hardy-Littlewood's result in uniformly John domains.

2000 Mathematics Subject Classification: 30C65.

Keywords: Quasiconformal mappings, Hölder continuity, growth of the derivative, uniformly John domains.

 

 

 

 

 

 

 

 

 

 

 

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