Continuous sparse domination and dimensionless weighted estimates for the Bakry Riesz vector
Abstract
We present a fundamentally new proof of the dimensionless Lp boundedness of the Bakry Riesz vector on manifolds with bounded geometry. Our proof has the significant advantage that it allows for a much stronger conclusion than previous arguments, namely that of some new dimensionless weighted estimates with optimal exponent. Part of the importance of this task lies in the novelty of the techniques: we develop the self similarity argument known as sparse domination in the setting of uniformly integrable cadlag Hilbert space valued martingales and extend the domination to a process with infinite memory. We provide a range of optimal weighted estimates and weak type estimates for these stochastic processes. Previous geometric Riesz transform estimates relied on Bellman functions and did not provide this range of weighted estimates. The development of sparse domination in this probabilistic setting and its use for high dimensional problems is new.
Cite
@article{arxiv.2211.10762,
title = {Continuous sparse domination and dimensionless weighted estimates for the Bakry Riesz vector},
author = {Komla Domelevo and Stefanie Petermichl and Kristina Ana Škreb},
journal= {arXiv preprint arXiv:2211.10762},
year = {2023}
}
Comments
This is a complete paper, contains part of arXiv:1607.06319 and extends the scope of arXiv:1802.00366. The latter had a substantial gap we address. This version has the grant information added