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Bi-parameter paraproducts by Muscalu, Camil; Pipher, Jill; Tao, Terence; Thiele, Christoph is a scholarly article available to read on EtoBox.

What is Bi-parameter paraproducts about?

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.

Author

Muscalu, Camil; Pipher, Jill; Tao, Terence; Thiele, Christoph

Published

2003

Language

EN