Principal values for Riesz transforms and rectifiability
| dc.creator | Tolsa, Xavier | |
| dc.date | 2007-08-01 | |
| dc.date.accessioned | 2026-07-07T08:21:43Z | |
| dc.date.available | 2026-07-07T08:21:43Z | |
| dc.description | Let $E\subset R^d$ with $H^n(E)<\infty$, where H^n stands for the $n$-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit $$\lim_{\ve\to0}\int_{y\in E:|x-y|>\ve} \frac{x-y}{|x-y|^{n+1}} dH^n(y)$$ exists H^n-almost everywhere in E. To prove this result we obtain precise estimates from above and from below for the $L^2$ norm of the n-dimensional Riesz transforms on Lipschitz graphs. | |
| dc.description | 47 pages | |
| dc.identifier | https://arxiv.org/abs/0708.0109 | |
| dc.identifier | http://arxiv.org/abs/0708.0109 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135408 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Functional Analysis | |
| dc.subject | 42B20, 28A75 | |
| dc.title | Principal values for Riesz transforms and rectifiability | |
| dc.type | text |