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Bi-parameter paraproducts

Camil Muscalu·Jill Pipher·Terence Tao·Christoph Thiele
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Abstract

In the first part of the paper we prove a bi-parameter version of a well known multilinear theorem of Coifman and Meyer. As a consequence, we generalize the Kato-Ponce inequality in nonlinear PDE, obtaining a fractional Leibnitz rule for derivatives in the $x_1$ and $x_2$ directions simultaneously. Then, we show that the double bilinear Hilbert transform does not satisfy any $L^p$ estimates.

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Camil Muscalu, Jill Pipher, Terence Tao, Christoph Thiele. 2013-03-20. Bi-parameter paraproducts. https://arxiv.org/abs/math/0310367

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