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Paraproducts in one and several parameters
-
Michael Lacey
and
Jason Metcalfe
Published/Copyright:
March 12, 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.
Received: 2005-09-12
Published Online: 2007-03-12
Published in Print: 2007-03-20
© Walter de Gruyter
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Articles in the same Issue
- P-adic logarithmic forms and group varieties III
- Moving homology classes to infinity
- On a class of locally finite T-groups
- On Ext-universal modules in Gödel's universe
- Paraproducts in one and several parameters
- Labeled configuration spaces and group completions
- Universal localizations embedded in power-series rings
Articles in the same Issue
- P-adic logarithmic forms and group varieties III
- Moving homology classes to infinity
- On a class of locally finite T-groups
- On Ext-universal modules in Gödel's universe
- Paraproducts in one and several parameters
- Labeled configuration spaces and group completions
- Universal localizations embedded in power-series rings
