Fiber-wise Calder\'on-Zygmund decomposition and application to a bi-dimensional paraproduct

Abstract

We are interested in a new kind of bi-dimensional bilinear paraproducts (appearing in [6]), which do not fit into the setting of bilinear Calder\'on-Zygmund operators. In this paper we propose a fiber-wise Calder\'on-Zygmund decomposition, which is specially adapted to this kind of bi-dimensional paraproduct.