Hardy spaces and a Walsh model for bilinear cone operators

Abstract

The study of bilinear operators associated to a class of non-smooth symbols can be reduced to ther study of certain special bilinear cone operators to which a time frequency analysis using smooth wave-packets is performed. In this paper we prove that when smooth wave-packets are replaced by Walsh wave-packets the corresponding discrete Walsh model for the cone operators is not only L p L^{p} -bounded, as Thiele has shown in his thesis for the Walsh model corresponding to the bilinear Hilbert transform, but actually improves regularity as it maps into a Hardy space. The same result is expected to hold for the special bilinear cone operators.