A family of convolution operators, part two

TL;DR

This paper introduces a new approach to Bochner-Riesz summability by studying a family of convolution operators with Fourier multipliers linked to distributions singular on the light-cone.

Contribution

It presents a novel method connecting convolution operators with light-cone singularities to improve understanding of Bochner-Riesz summability.

Findings

New Fourier multiplier framework for convolution operators

Enhanced understanding of Bochner-Riesz summability

Connections between distributions and summability methods

Abstract

We study a family of convolution operators. Their regarding Fourier multipliers are defined in terms of distributions having singularity on the light-cone in $\mathbb{R}^{n+1}$. As a result, we give a new approach to the Bochner-Riesz summability.