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Paraproducts in One and Several Parameters

Michael T Lacey·Jason Metcalfe
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Abstract

For multiparameter bilinear paraproduct operators $B$ we prove the estimate $$ B: L^p X L^q --> L^r, 1<p,q\le{}\infty. $$ Here, $1/p+1/q=1/r$ and special attention is paid to the case of $0<r<1$. (Note that the families of multiparameter paraproducts are much richer than in the one parameter case.) These estimates are the essential step in the version of the multiparameter Coifman-Meyer theorem proved by C. Muscalu, J. Pipher, T. Tao, and C. Thiele. We offer a different proof of these inequalities.

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Michael T Lacey, Jason Metcalfe. 2005-08-09. Paraproducts in One and Several Parameters. https://arxiv.org/abs/math/0502334

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