Lp and weak L1 estimates for the maximal Riesz transform and the maximal Beurling transform
Classical Analysis and ODEs
2010-12-21 v1
Abstract
We estimate in Lp the maximal Riesz transform in terms of the Riesz transform itself for p greater than 1. In the limiting case p=1 the weak L1 inequality is shown to fail. Surprisingly, the weak L1 inequality for the maximal Beurling transform in terms of the Beurling transform does hold.
Cite
@article{arxiv.math/0603077,
title = {Lp and weak L1 estimates for the maximal Riesz transform and the maximal Beurling transform},
author = {Joan Mateu and Joan Verdera},
journal= {arXiv preprint arXiv:math/0603077},
year = {2010}
}
Comments
12 pages