Bi-parameter paraproducts

Details Bi-parameter paraproducts Bi-parameter paraproducts

2003-10-23

arxiv.org/abs/math/0310367v1

Mathematics

Classical Analysis and ODEs

26 pages; no figures; submitted, Acta Math

Scientific paper

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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