Weighted decoupling estimates and the Bochner-Riesz means

TL;DR

This paper establishes new weighted decoupling estimates and applies them to improve convergence conditions for Bochner-Riesz means of functions in certain L^p spaces in low dimensions.

Contribution

It introduces novel weighted decoupling estimates and enhances the understanding of Bochner-Riesz means convergence for 1<p<2 in 2D and 3D.

Findings

Improved convergence conditions for Bochner-Riesz means.

New weighted decoupling estimates.

Enhanced understanding of harmonic analysis in low dimensions.

Abstract

We prove new weighted decoupling estimates. As an application, we give an improved sufficient condition for almost everywhere convergence of the Bochner-Riesz means of arbitrary $L^p$ functions for $1<p<2$ in dimensions 2 and 3.