R^3上一类特殊Besicovitch集的维数估计  

ESTIMATES OF DIMENSION FOR A TYPE OF SPECIAL BESICOVITCH SETS IN R^3

作　　者：陈泽斌 CHEN Ze-bin(School of Mathematics,Shantou University,Shantou 515063,China)

机构地区：[1]汕头大学数学系,广东汕头515063

出　　处：《数学杂志》2020年第4期493-497,共5页Journal of Mathematics

摘　　要：本文研究了R^3上一类圆盘型Besicovitch集的Hausdorff维数问题.将Kakeya问题二维情形的其中一种证明方法推广到R^3空间,获得了该类圆盘型Besicovitch集的Hausdorff维数为3.This dissertation is devoted to the Hausdorff dimension for a type of disc Besicovitch sets.It is well know that the situation of R^2 about Kakeya problem has been solved by now,and there exist several methods which can prove it,which aim to generalize one of those methods to R^3 space.Then we prove that there are a type of disc Besicovitch sets in R^3 whose Hausdorff dimension is 3.

关 键 词：Besicovitch集 Kakeya问题 HAUSDORFF维数 

分 类 号：O174.1[理学—数学]