Orthogonal projections of discretized sets

被引：11
作者：
He, Weikun [1 ,2 ]
机构：
[1] Univ Paris Saclay, Univ Paris Sud, Lab Math Orsay, F-91405 Orsay, France
[2] Hebrew Univ Jerusalem, Einstein Inst Math, IL-91904 Jerusalem, Israel
来源：
JOURNAL OF FRACTAL GEOMETRY | 2020年 / 7卷 / 03期
关键词：
Projection theorem; discretized set; Hausdorff dimension; HAUSDORFF DIMENSION; RESTRICTED FAMILIES; PRODUCT;
D O I：
10.4171/JFG/92
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We generalize Bourgain's discretized projection theorem to higher rank situations. Like Bourgain's theorem, our result yields an estimate for the Hausdorff dimension of the exceptional sets in projection theorems formulated in terms of Hausdorff dimensions. This estimate complements earlier results of Mattila and Falconer.
引用
收藏
页码：271 / 317
页数：47
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