Variational inequalities for the commutators of rough operators with BMO functions
Classical Analysis and ODEs
2017-09-12 v1
Abstract
In this paper, starting with a relatively simple observation that the variational estimates of the commutators of the standard Calder\'on-Zygmund operators with the BMO functions can be deduced from the weighted variational estimates of the standard Calder\'on-Zygmund operators themselves, we establish similar variational estimates for the commutators of the BMO functions with rough singular integrals which do not admit any weighted variational estimates. The proof involves many Littlewood-Paley type inequalities with commutators as well as Bony decomposition and related para-product estimates.
Keywords
Cite
@article{arxiv.1709.03125,
title = {Variational inequalities for the commutators of rough operators with BMO functions},
author = {Yanping Chen and Yong Ding and Guixiang Hong and Honghai Liu},
journal= {arXiv preprint arXiv:1709.03125},
year = {2017}
}
Comments
27 pages