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