ON A CLASS OF BESICOVITCH FUNCTIONS TO HAVE EXACT BOX DIMENSION: A NECESSARY AND SUFFICIENT CONDITION

作     者：ZhouSongping HeGuolong 

作者机构：ZhejiangInstituteofScienceandTechnologyChinaNingboUniversityChina ZhejiangNormalUniversityChina 

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

年 卷 期：2004年第20卷第2期

页      面：175-181页

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

基　　金：Research supported by national Natural Science Foundation of China (10141001) Zhejiang Provincial Natural Science Foundation 9100042 and 1010009 

主　　题：Weierstrass function Besicovitch function fractal dimension box dimension Hard- mard condition 

摘      要：This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given by where 1 tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ1. The results show that is a necessary and sufficient condition for Graph(B(t)) to have same upper and lower box dimensions. For the fractional Riemann-Liouvtlle differential operator Du and the fractional integral operator D-v, the results show that if A is sufficiently large, then a necessary and sufficient condition for box dimension of Graph(D-v(B)), 0 v s - 1, to be s - v and box dimension of Graph(Du(B)), 0 u 2 - s, to be s + u is also lim.