Bi-parameter paraproducts

Camil Muscalu; Jill Pipher; Terence Tao; Christoph Thiele

Bi-parameter paraproducts

Classical Analysis and ODEs 2013-03-22 v2

Authors: Camil Muscalu , Jill Pipher , Terence Tao , Christoph Thiele

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.

Cite

@article{arxiv.math/0310367,
  title  = {Bi-parameter paraproducts},
  author = {Camil Muscalu and Jill Pipher and Terence Tao and Christoph Thiele},
  journal= {arXiv preprint arXiv:math/0310367},
  year   = {2013}
}

Comments

26 pages; no figures. A missing hypothesis on the exponents in some of the estimates, pointed out to us by Loukas Grafakos and Seungly Oh, has been added

Bi-parameter paraproducts

Abstract

Cite

Comments

Related papers