Some remarks on bilinear Littlewood–Paley theory

In this work, some bilinear analogues of linear Littlewood–Paley theory are explored. Paraproducts with functions decomposed at different scales are shown to be bounded on certain products of Lebesgue spaces. Results concerning square functions associated with smooth and nonsmooth cutoffs are also obtained.  2005 Elsevier Inc. All rights reserved.