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

作　　者：ZhouSongping HeGuolong 

机构地区：[1]ZhejiangInstituteofScienceandTechnology,ChinaNingboUniversity,China [2]ZhejiangNormalUniversity,China

出　　处：《Analysis in Theory and Applications》2004年第2期175-181,共7页分析理论与应用（英文刊）

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

摘　　要：This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given bywhere 1 < s < 2, λk> tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ>1. The results show thatis 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 dimensionof Graph(D-v(B)), 0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)), 0 < u < 2 - s, to bes + u is also lim.This paper summarized recent achievements obtained by the authors about the box dimensions of the Besicovitch functions given bywhere 1 < s < 2, λk> tends to infinity as k→∞ and λk satisfies λk+1/λk≥λ>1. The results show thatis 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 dimensionof Graph(D-v(B)), 0 < v < s - 1, to be s - v and box dimension of Graph(Du(B)), 0 < u < 2 - s, to bes + u is also lim.

关 键 词：Weierstrass function Besicovitch function fractal dimension box dimension Hard- mard condition 

分 类 号：O175.3[理学—数学]