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arXiv · 1505.07947

Bloom's Inequality: Commutators in a Two-Weight Setting

Irina Holmes·Michael T. Lacey·Brett D. Wick
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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 Calder\'on-Zygmund operators and dimensions.

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Irina Holmes, Michael T. Lacey, Brett D. Wick. 2015-05-29. Bloom's Inequality: Commutators in a Two-Weight Setting. https://doi.org/10.1007/s00013-015-0840-8

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