Zygmund微分映射的正则点

数学物理学报

Zygmund微分映射的正则点

徐栩;张运涛

武汉大学数学与统计学院武汉 430072

收稿日期:2005-10-08 修回日期:2006-11-08 出版日期:2008-02-25 发布日期:2008-02-25
通讯作者: 徐栩
基金资助:
国家自然科学基金(10261002, 10371047)资助

On the Regular Points of Zygmund Differentiable Maps

Xu Xu;Zhang Yuntao

School of Mathematics and Statistics, Wuhan University, Wuhan 430072

Received:2005-10-08 Revised:2006-11-08 Online:2008-02-25 Published:2008-02-25
Contact: Xu Xu

摘要/Abstract

摘要： 该文的主要结果是: 对任意Zygmund类$C^{p,Z}$映射$f:R^{n}\rightarrow R^{m}$, 若$\frac{n-m}{2}\leq p\leq n-m-1$, 则有mes$K_{f}>0$或者mes$C_{f}>0$. 这个结果给出了Hirsch问题的部分回答.

关键词: 正则点, 可微性, Zygmund类

Abstract:

The main result of this article is: For any Zygmund class $C^{p,Z}$
map $f:R^{n}\rightarrow R^{m}$ if $\frac{n-m}{2}\leq p\leq n-m-1$, then either mes$K_{f}>0$ or mes$C_{f}>0$. It provides a partial answer of the Hirsch Problem.

Key words: Regular points, Differentiability, Zygmund class

中图分类号:

58C25

徐栩;张运涛. Zygmund微分映射的正则点[J]. 数学物理学报, 2008, 28(1): 35-038.

Xu Xu;Zhang Yuntao. On the Regular Points of Zygmund Differentiable Maps[J]. Acta mathematica scientia,Series A, 2008, 28(1): 35-038.