On A. Zygmund differentiation conjecture
| dc.creator | Assani, I. | |
| dc.date | 2006-09-28 | |
| dc.date.accessioned | 2026-07-07T07:25:25Z | |
| dc.date.available | 2026-07-07T07:25:25Z | |
| dc.description | Consider $v$ a Lipschitz unit vector field on $R^n$ and $K$ its Lipschitz constant. We show that the maps $S_s:S_s(X) = X + sv(X)$ are invertible for $0\leq |s|<1/K$ and define nonsingular point transformations. We use these properties to prove first the differentiation in L^p norm for $1\le p<\infty.$ Then we show the existence of a universal set of values $s\in [-1/2K,1/2K]$ of measure 1/K for which the Lipschitz unit vector fields $v\circ S_s^{-1}$ satisfy Zygmund's conjecture for all functions in $L^p(\R^n)$ and for each p, $1\leq p< \infty.$ | |
| dc.description | Preliminary version | |
| dc.identifier | https://arxiv.org/abs/math/0609827 | |
| dc.identifier | http://arxiv.org/abs/math/0609827 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/116710 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42B25 | |
| dc.title | On A. Zygmund differentiation conjecture | |
| dc.type | text |