On the Hilbert transform and lacunary directions in the plane

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

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.
11 pages, 1 fiure. This is version to appear in Illinois J. Math

Keywords

Classical Analysis and ODEs, 42b20

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/60168

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0010196
 http://arxiv.org/abs/math/0010196

Collections

arXiv