On the Hilbert transform and lacunary directions in the plane
| dc.creator | Lacey, Michael T. | |
| dc.date | 2000-10-20 | |
| dc.date | 2001-12-21 | |
| dc.date.accessioned | 2026-07-07T04:38:09Z | |
| dc.date.available | 2026-07-07T04:38:09Z | |
| dc.description | Let $H_k$ be the one dimensional Hilbert transform computed in the direction $(1,2^k)$ in the plane. We show that the maximal operator $\sup_k |H_kf|$ maps $L^p$ of the plane into itself for $1<p<\infty$. The same result with the Hilbert transform replaced by the one dimensional maximal function was proved by Nagel, Stein and Wainger in 1978. | |
| dc.description | 11 pages, 1 fiure. This is version to appear in Illinois J. Math | |
| dc.identifier | https://arxiv.org/abs/math/0010196 | |
| dc.identifier | http://arxiv.org/abs/math/0010196 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60168 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 42b20 | |
| dc.title | On the Hilbert transform and lacunary directions in the plane | |
| dc.type | text |