Paraproducts in One and Several Parameters

Abstract

For multiparameter bilinear paraproduct operators $B$ we prove the estimate $$B:L^{p}X{L}^q-->L^r,1<p,q\le \infty .$$ 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. We offer a different proof of these inequalities.

Minor corrections made