Multiparameter Riesz commutators

Michael T. Lacey; Stefanie Petermichl; Jill C. Pipher; Brett D. Wick

doi:10.1353/ajm.0.0059

Multiparameter Riesz commutators

Michael T. Lacey, Stefanie Petermichl, Jill C. Pipher, Brett D. Wick

Department of Mathematics & Statistics

Research output: Contribution to journal › Article › peer-review

40 Scopus citations

Abstract

It is shown that product BMO of S.-Y. A. Chang and R. Fefferman, defined on the space ℝ ^d1 ℝ ^dt, can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of R. Coifman, R. Rochberg, and G. Weiss, and at the same time extends the work of M. Lacey and S. Ferguson and M. Lacey and E. Terwilleger, on multiparameter commutators with Hilbert transforms.

Original language	English
Pages (from-to)	731-769
Number of pages	39
Journal	American Journal of Mathematics
Volume	131
Issue number	3
DOIs	https://doi.org/10.1353/ajm.0.0059
State	Published - 2009

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abstract = "It is shown that product BMO of S.-Y. A. Chang and R. Fefferman, defined on the space ℝ d1 ℝ dt, can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of R. Coifman, R. Rochberg, and G. Weiss, and at the same time extends the work of M. Lacey and S. Ferguson and M. Lacey and E. Terwilleger, on multiparameter commutators with Hilbert transforms.",

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AU - Petermichl, Stefanie

AU - Pipher, Jill C.

AU - Wick, Brett D.

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AB - It is shown that product BMO of S.-Y. A. Chang and R. Fefferman, defined on the space ℝ d1 ℝ dt, can be characterized by the multiparameter commutators of Riesz transforms. This extends a classical one-parameter result of R. Coifman, R. Rochberg, and G. Weiss, and at the same time extends the work of M. Lacey and S. Ferguson and M. Lacey and E. Terwilleger, on multiparameter commutators with Hilbert transforms.

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DO - 10.1353/ajm.0.0059

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JO - American Journal of Mathematics

JF - American Journal of Mathematics

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ER -

Multiparameter Riesz commutators

Abstract

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