Bloom’s inequality: commutators in a two-weight setting
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In 1985, Bloom characterized the boundedness of the commutator [b, H] as a map between a pair of weighted L p spaces, where both weights are in A p . The characterization is in terms of a novel BMO condition. We give a ‘modern’ proof of this result, in the case of p = 2. In a subsequent paper, this argument will be used to generalize Bloom’s result to all Calderón–Zygmund operators and dimensions.
KeywordsCommutators Calderón–Zygmund operators BMO Weights Haar multiplier Paraproducts
Mathematics Subject ClassificationPrimary 42A 42B Secondary 42A40 42A99 42B35 42B20 42B30
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