[1]王朝祥,黄心中.闭区间上Zygmund函数的延拓定理[J].华侨大学学报(自然科学版),2006,27(2):119-122.[doi:10.3969/j.issn.1000-5013.2006.02.002]
　Wang Chaoxiang,Huang Xinzhong.On the Extension Theorem for Zygmund Functions in Closed Interval[J].Journal of Huaqiao University(Natural Science),2006,27(2):119-122.[doi:10.3969/j.issn.1000-5013.2006.02.002]
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闭区间上Zygmund函数的延拓定理()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第27卷
期数:
2006年第2期
页码:
119-122
栏目:
出版日期:
2006-04-20

文章信息/Info

Title:
On the Extension Theorem for Zygmund Functions in Closed Interval
文章编号:
1000-5013(2006)02-0119-04
作者:
王朝祥; 黄心中
华侨大学数学系; 华侨大学数学系 福建 泉州 362021; 福建 泉州 362021
Author(s):
Wang Chaoxiang;  Huang Xinzhong
Department of Mathematics, Huaqiao University, 362021, Quanzhou, China
关键词:
Zygmund函数;  拟共形变形;  拟共形映照;  延拓
Keywords:
Zygmund function;  quasiconformal deformation;  quasiconformal mapping;  extension
分类号:
O174.55
DOI:
10.3969/j.issn.1000-5013.2006.02.002
文献标志码:
A
摘要:
设f(x)是闭区间I上的连续函数,f(x)为I上的Zygmund函数.如果存在常数C≥0,使得f(x)满足|f(x+t)-2f(x)+f(x-t)|0成立.可将其延拓成上的Zygmund函数的充分条件,并估计其范数‖f‖z.
Abstract:
Let f(x) be continuous on closed interval I,f(x) is called a Zygmund function on I if there exists one constant C≥0 such that |f(x+t)-2f(x)+f(x-t)|＜Ct for all x,x±∈ I and for t＞0. We give sufficient condition for such Zygmund function which can be extended to a Zygmund function on (?) and give estimation for its norm ‖f‖_z.

参考文献/References:

[1] Baladi V, Jiang Y P, Lanford O E. Transfer operators acting on Zygmund functions [J]. Transactions of the American Mathematical Society, 1996(4):1599-1615.doi:10.1090/S0002-9947-96-01599-1.
[2] Huang Xinzhong, Oh S K, Jun E P. On the maximum value for Zygmund class on an interval [J]. IJMMS, 2002(2):65-71.
[3] 王朝祥, 黄心中. Zygmund函数在闭区间上最大值的估计 [J]. 数学研究, 2005(1):66-70.doi:10.3969/j.issn.1006-6837.2005.01.010.
[4] Gardiner F, Sullivan D. Symmetric structures on a closed curve [J]. American Journal of Mathematics, 1992, (114):683-736.doi:10.2307/2374795.
[5] Reich E, Chen J. Extensions with bounded (e)--derivative [J]. Annales Academic Scientiarum Fennicae Mathematica, 1991.377-389.
[6] Beurling A, Ahlfors L. The boundary correspondence under quasiconformal mappings [J]. Acta Mathematica, 1956.125-142.doi:10.1007/BF02392360.
[7] Duren P L. Theory of Hp spaces [M]. New York:Academic Press, 1970.91.

备注/Memo

备注/Memo:
福建省自然科学基金资助项目(Z0511025)
更新日期/Last Update: 2014-03-23