2017/12/19 by Natalia Accomazzo, Accomazzo, Natalia, Javier C. Martínez-Perales +3 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA
paper · pdf · doi:10.48550/arxiv.1712.06923
18 pages
arxiv created 2017/12/19 · arxiv updated 2017/12/20
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 Bényi, Martell, Moen, Stachura, Torres and establish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space.