On the Local $ Tb$ Theorem under Minimal Integrability
Classical Analysis and ODEs
2012-06-19 v2
Abstract
We prove a version of the local Tb Theorem assuming that the accretive functions b_Q and T b_Q are locally L ^{p} integrable, for any 1< p < \infty . This improves a recent result of Hytonen-Nazarov. The proof strategy relies upon the their strategy, with additional techniques concerning twisted martingale differences and the use of random dyadic grids in the local Tb setting.
Cite
@article{arxiv.1206.2861,
title = {On the Local $ Tb$ Theorem under Minimal Integrability},
author = {Michael T Lacey and Antti V Vähäkangas},
journal= {arXiv preprint arXiv:1206.2861},
year = {2012}
}
Comments
The argument fails, due to a casual use of the classical Cotlar inequality