Multiparameter Riesz Commutators

Details Multiparameter Riesz Commutators Multiparameter Riesz Commutators

2007-04-27

arxiv.org/abs/0704.3720v2

Amer. J. Math. 131 (2009), no. 3, 731-769

Mathematics

Classical Analysis and ODEs

38 Pages. References updated. To appear in American J Math

Scientific paper

10.1353/ajm.0.0059

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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