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Beurling-Ahlfors延拓的伸张函数之估计

Estimating Dilatation Function of Beurling-Ahlfors Extension
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摘要 研究实轴R1上的保向同胚映照到上半平面Beurling Ahlfors延拓的伸张函数的性质 .通过证明几个不等式 ,对伸张函数D(z)作进一步的估计 ,改进了相关的结果 . With regard to Beurling-Ahlfors extension from sense-preserving homeomorphism on real axis R 1 to the upper half plane, the authors make a study on the properties of its dilatation function; and form a further estimate of dilatation function D(z) through proving several inequalities by which some known results are improved.
机构地区 华侨大学数学系
出处 《华侨大学学报(自然科学版)》 CAS 2004年第2期126-129,共4页 Journal of Huaqiao University(Natural Science)
基金 国务院侨务办公室重点科研基金资助项目 (0 1QZR0 1)
关键词 Beurling-Ahlfors延拓 伸张函数 拟对称函数 保向同胚映照 Beurling-Ahlfors extension, dilatation function, quasi-symmetric function
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参考文献4

  • 1Ahlfors L V. Lectures on Quasiconformal Mappings[M]. New York: Nostrand Company, 1966. 63~73
  • 2Lehtinen M. The dilatation of Beurling-Ahlfors extension of quasisymmetric functions[J]. Ann. Acad. Sci. Fenn. Ser. AI Math., 1983, 8(1): 187~191
  • 3Chen Jixiu, Chen Zhiguo, He Chengqi. Boundary Correspondence under u(z)-Homeomorphisms[J]. Michigan Math. J., 1996, 43: 211~220
  • 4郑学良.Beurling-Ahlfors扩张的伸张函数与ID-同胚[J].数学学报(中文版),2002,45(5):1035-1040. 被引量:9

二级参考文献8

  • 1Ahlfors L. V., Lectures on Quasiconformal Mappings, New York: Nostrand Company, 1966.
  • 2Beurling A., Ahlfors L. V., The boundary correspondence under quasiconformal mappings, Acta. Math., 1956, 96: 125-142.
  • 3Chen Z. G., Boundary behavior of the dilatation of the Beurling-Ahlfors extension, Journal of Fudan Univer sity (Natural Science), 1996, 35(4): 381-386.
  • 4Fang A. N., Generalized Beurling-Ahlfors theorem, Science in China, Ser. A, 1995, 25(6): 565-572 (in Chinese).
  • 5Fang A. N., On the compactness of Homemorphisms with Integrable Dilatations, Acta Mathematica Sinica,1998, 41(3): 463-466 (in Chinese).
  • 6Lehtinen M., The dilatation of Beurling-Ahlfors extension of quasisymmetric functions, Ann. Acad. Sci.Fenn. Ser AI Math., 1983, 8(1): 187-191.
  • 7Zheng S. Z., Beltrami systems with Double characteristic Matrices and Quasiregular Mappings, Acta Math-ematica Sinica, 1997, 40(5): 745-750 (in Chinese).
  • 8Zheng S. Z., Partial regularity for A-harmonic systems and quasiregular mappings, Chinese Journal ofContemporary Mathematics, 1998, 19(1): 19-30.

共引文献8

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