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arXiv · 0704.3720

Multiparameter Riesz Commutators

Michael Lacey·Stefanie Petermichl·Jill Pipher·Brett Wick
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Abstract

It is shown that product BMO of Chang and Fefferman, defined on the product of Euclidean spaces can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of Coifman, Rochberg, and Weiss, and at the same time extends the work of Lacey and Ferguson and Lacey and Terwilleger on multiparameter commutators with Hilbert transforms. The method of proof requires the real-variable methods throughout, which is new in the multi-parameter context.

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Michael Lacey, Stefanie Petermichl, Jill Pipher, Brett Wick. 2007-04-27. Multiparameter Riesz Commutators. https://doi.org/10.1353/ajm.0.0059

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