A class of singular bilinear maximal functions

TL;DR

This paper establishes Lebesgue space bounds for certain singular bilinear maximal functions on the real line, using a combination of smoothing inequalities and Calderón-Zygmund theory.

Contribution

It introduces new bounds for bilinear maximal functions and combines advanced techniques, including a trilinear smoothing inequality and Calderón-Zygmund theory.

Findings

Lebesgue space bounds for bilinear maximal functions established

Use of trilinear smoothing inequality in the proof

Application of Calderón-Zygmund theory to bilinear operators

Abstract

Lebesgue space bounds $L^{p_1}({\mathbb R}^1) \times L^{p_2}(^1) \to L^q({\mathbb R}^1)$ are established for certain maximal bilinear operators. The proof combines a trilinear smoothing inequality with Calder\'on-Zygmund theory. A reference to overlapping work of other authors on one observation has been added.