Forum Mathematicum

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Issue: Mar 2007

Forum Mathematicum
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Forum Mathematicum

ISSN (Print) 0933-7741

ISSN (Online) 1435-5337

DOI 10.1515/form.407

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Issue: Mar 2007

Volume 19, Number 2

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Paraproducts in one and several parameters

Michael Lacey1,

1School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332 USA.

Jason Metcalfe2

2Department of Mathematics, University of California, Berkeley, CA 94720-3840 USA.

Citation Information. Forum Mathematicum. Volume 19, Issue 2, Pages 325–351, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/FORUM.2007.013, March 2007
Publication History: Received: 12/09/2005; published online: 12/03/2007

Abstract

For multiparameter bilinear paraproduct operators B we prove the estimate
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 [Mucalu Camil, Pipher Jill, Tao Terrance, and Thiele Christoph: Bi-parameter paraproducts. Acta Math. 193 (2004), 269–296, Mucalu Camil, Pipher Jill, Tao Terrance, and Thiele Christoph: Multi-parameter paraproducts. arxiv:math.CA/0411607]. We offer a different proof of these inequalities.

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