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arXiv · 1712.06923

On Bloom type estimates for iterated commutators of fractional integrals

Natalia Accomazzo·Javier C. Martínez-Perales·Israel P. Rivera-Ríos
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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 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.

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Natalia Accomazzo, Javier C. Martínez-Perales, Israel P. Rivera-Ríos. 2017-12-19. On Bloom type estimates for iterated commutators of fractional integrals. https://arxiv.org/abs/1712.06923

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