HAUSDORFF DIMENSION AND DISTANCE SETS

被引：50

作者：

Bourgain, Jean ^{[1
]}

机构：

[1] Inst Hautes Etud Sci, Dept Math, F-91440 Bures Sur Yvette, France

来源：

ISRAEL JOURNAL OF MATHEMATICS | 1994年 / 87卷 / 1-3期

关键词：

D O I：

10.1007/BF02772994

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

According to a result of K. Falconer (1985), the set D(A) = {vertical bar x - y vertical bar; x, y is an element of A} of distances for a Souslin get A of R-n has positive 1-dimensional measure provided the Hausdorff dimension of A is larger than (n+1)/2.* We give an improvement of this statement in dimensions n = 2, n = 3. The method is based on the fine theory of Fourier restriction phenomena to spheres. Variants of it permit further improvements which we don't plan to describe here. This research originated from some discussions with P. Mattila on the subject.

引用

页码：193 / 201

页数：9

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[5] SPHERICAL AVERAGES OF FOURIER-TRANSFORMS OF MEASURES WITH FINITE-ENERGY - DIMENSION OF INTERSECTIONS AND DISTANCE SETS [J].

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