Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592812 | Journal of Functional Analysis | 2008 | 53 Pages |
Abstract
Let E⊂RdE⊂Rd with Hn(E)<∞Hn(E)<∞, where HnHn stands for the n-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limitlimε→0∫y∈E:|x−y|>εx−y|x−y|n+1dHn(y) exists HnHn-almost everywhere in E . To prove this result we obtain precise estimates from above and from below for the L2L2 norm of the n-dimensional Riesz transforms on Lipschitz graphs.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xavier Tolsa,