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Archiv der Mathematik

, Volume 106, Issue 1, pp 53–63 | Cite as

Bloom’s inequality: commutators in a two-weight setting

  • Irina Holmes
  • Michael T. Lacey
  • Brett D. Wick
Article

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.

Keywords

Commutators Calderón–Zygmund operators BMO Weights Haar multiplier Paraproducts 

Mathematics Subject Classification

Primary 42A 42B Secondary 42A40 42A99 42B35 42B20 42B30 

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Copyright information

© Springer International Publishing 2015

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  2. 2.Department of MathematicsWashington University-Saint Louis, One Brookings DriveSaint LouisUSA

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