Sparse bilinear forms for Bochner Riesz multipliers and applications

TL;DR

This paper applies a recent sparse bilinear form approach to analyze Bochner-Riesz operators, leading to new weighted estimates and vector-valued inequalities in harmonic analysis.

Contribution

It introduces a novel application of sparse bilinear forms to Bochner-Riesz multipliers, extending recent methods to obtain quantitative weighted and vector-valued bounds.

Findings

Derived new weighted estimates for Bochner-Riesz operators.

Established vector-valued inequalities using sparse bilinear forms.

Extended recent approaches to a broader class of harmonic analysis operators.

Abstract

We use the very recent approach developed by Lacey in [23] and extended by Bernicot-Frey-Petermichl in [3], in order to control Bochner-Riesz operators by a sparse bilinear form. In this way, new quantitative weighted estimates, as well as vector-valued inequalities are deduced.