Abstract
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.
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M. T. Lacey’s research was supported in part by National Science Foundation DMS Grant #1265570. B. D. Wick’s research was supported in part by National Science Foundation DMS Grants #0955432 and #1560955.
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Holmes, I., Lacey, M.T. & Wick, B.D. Bloom’s inequality: commutators in a two-weight setting. Arch. Math. 106, 53–63 (2016). https://doi.org/10.1007/s00013-015-0840-8
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DOI: https://doi.org/10.1007/s00013-015-0840-8