Off-diagonal sharp two-weight estimates for sparse operators

Fackler, Stephan; Hytönen, Tuomas P.

doi:10.48550/arxiv.1711.08274

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2017

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“…and that is, up until now (see [10]), the smallest constant characterizing the A ∞ class. We would like to point out that it would be possible to provide mixed estimates for (I α ) m b in terms of this A ∞ constant.…”

Section: Letmentioning

confidence: 96%

On Bloom type estimates for iterated commutators of fractional integrals

Accomazzo¹,

Martínez-Perales²,

Rivera-Rı́os³

2017

Preprint

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In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from [15]. 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 the recent paper [22]. We extend as well the necessity established in [15] to iterated commutators providing a new proof. As a consequence of the preceding results we recover the one weight estimates in [7, 1] and establish the sharpness in the iterated case. Our result provides as well a new characterization of the BMO space.

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Section: Letmentioning

confidence: 96%