On Bloom type estimates for iterated commutators of fractional integrals
Abstract
In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from a work of Holmes, Rahm and Spencer. We give new proofs for those inequalities relying upon a new sparse domination that we provide as well in this paper and also in techniques developed in a recent paper due to Lerner, Ombrosi and the third author. We extend as well the necessity established in the work of Holmes, Rahm and Spencer to iterated commutators providing a new proof. As a consequence of the preceding results we recover the one weight estimates in works of Cruz-Uribe and Moen and B\'enyi, Martell, Moen, Stachura, Torres and establish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space.
Keywords
Cite
@article{arxiv.1712.06923,
title = {On Bloom type estimates for iterated commutators of fractional integrals},
author = {Natalia Accomazzo and Javier C. Martínez-Perales and Israel P. Rivera-Ríos},
journal= {arXiv preprint arXiv:1712.06923},
year = {2017}
}
Comments
18 pages