Lp estimates for non smooth bilinear Littlewood-Paley square functions on R

TL;DR

This paper investigates non-smooth bilinear Littlewood-Paley square functions on the real line, establishing their boundedness in Lebesgue spaces and relating them to bilinear Hilbert transforms.

Contribution

It introduces and analyzes non-smooth bilinear Littlewood-Paley square functions, providing new boundedness results and connections to bilinear Hilbert transforms.

Findings

Proved boundedness of bilinear square functions in Lebesgue spaces.

Established relationships between these operators and bilinear Hilbert transforms.

Extended classical linear results to bilinear, non-smooth contexts.

Abstract

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.