Some endpoint estimates for bilinear Coifman-Meyer multipliers

TL;DR

This paper investigates the boundedness of bilinear Coifman-Meyer multipliers on certain function spaces, leading to new endpoint inequalities and insights into products involving BMO and Hardy spaces.

Contribution

It establishes new mapping properties of bilinear Coifman-Meyer multipliers on endpoint and classical spaces, and derives related inequalities and product estimates.

Findings

Boundedness of bilinear Coifman-Meyer multipliers on $H^1$ and $L^p$ with BMO

New Kato-Ponce-type inequalities involving BMO

Pointwise product estimates for BMO with Hardy and $L^p$ functions

Abstract

In this paper we establish mapping properties of bilinear Coifman-Meyer multipliers acting on the product spaces $H^1(\mathbb{R}^n)\times\mathrm{bmo}(\mathbb{R}^n)$ and $L^p(\mathbb{R}^n)\times\mathrm{bmo}(\mathbb{R}^n)$, with $1<p<\infty$. As application of these results, we obtain some related Kato-Ponce-type inequalities involving the endpoint space $\mathrm{bmo}(\mathbb{R}^n)$, and we also study the pointwise product of a function in $\mathrm{bmo}(\mathbb{R}^n)$ with functions in $H^1(\mathbb{R}^n)$, $h^1(\mathbb{R}^n)$ and $L^p(\mathbb{R}^n)$, with $1<p<\infty$.