English

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.

Keywords

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

R2 v1 2026-07-22T17:32:23.271Z