A Local Property of Hausdorff Centered Measure of Self-Similar Sets

作     者：Zhiwei Zhu Zuoling Zhou 

作者机构：College of Mathematics and Statistics Zhaoqing University Lingnan College Sun Yat-Sen University 

出 版 物：《Analysis in Theory and Applications》 (分析理论与应用（英文刊）)

年 卷 期：2014年第30卷第2期

页      面：164-172页

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (No. 11371379) 

主　　题：Hausdorff centered measure Hausdorff measure self-similar sets. 

摘      要：We analyze the local behavior of the Hausdorff centered measure for self- similar sets. If E is a self-similar set satisfying the open set condition, then C^s（E∩B（x,r））≤（2r）^s for all x ∈ E and r〉 0, where Cs denotes the s-dimensional Hausdorff centered measure. The above inequality is used to obtain the upper bound of the Hausdorff centered measure. As the applications of above inequality, We obtained the upper bound of the Hausdorff centered measure for some self-similar sets with Hausdorff dimension equal to 1, and prove that the upper bound reach the exact Hausdorff centered measure.