Lp estimates for non smooth bilinear Littlewood-Paley square functions   on R
  In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. These bilinear operators are closely related to the bilinear Hilbert transforms and vector valued version of these ones. Mainly we prove boundedness-properties in Lebesgue spaces for them. 
Frederic Bernicot