Bilinear Littlewood-Paley for circle and transference

Abstract

In this paper we have obtained the boundedness of bilinear Littlewood-Paley operators on the circle group ${\mathbb T}$ by using appropriate transference techniques. In particular, bilinear analogue of Carleson's Littlewood-Paley result for all possible indices has been obtained. Also, we prove some bilinear analogues of de Leeuw's results concerning multipliers of ${\mathbb R}^n$.