Uniform estimates for paraproducts and related multilinear multipliers

TL;DR

This paper establishes uniform bounds for multilinear paraproduct operators across Lebesgue and Hardy spaces on R^d, considering variations in geometric and metric parameters.

Contribution

It introduces uniform estimates for multilinear paraproducts that are robust under changes in geometry and metrics on R^d.

Findings

Proved uniform Lebesgue and Hardy space estimates for multilinear operators

Achieved bounds that are stable under geometric and metric perturbations

Extended understanding of multilinear multipliers in variable geometric settings

Abstract

In this paper, we prove some uniform estimates between Lebesgue and Hardy spaces for operators closely related to the multilinear paraproducts on R^d. We are looking for uniformity with respect to parameters, which allow us to disturb the geometry and the metric on $R^d$.