$\mathbf{L}^p$-boundedness of the Bochner-Riesz operator

TL;DR

This paper introduces a new approach to Bochner-Riesz summability, demonstrating boundedness of the operator on L^p spaces within a specific range of p, advancing understanding of harmonic analysis.

Contribution

It provides a novel method to establish L^p-boundedness of the Bochner-Riesz operator for certain parameters, improving previous results in harmonic analysis.

Findings

Bochner-Riesz operator is bounded on L^p for specified p-range.

New approach simplifies the proof of boundedness.

Results extend the known range of p for boundedness.

Abstract

In this paper, we give a new approach to the Bochner-Riesz summability. As a result, we show that the Bochner-Riesz operator $\mathbf{S}^\delta, 0<\Re\delta<{1\over 2}$ is bounded on $\mathbf{L}^p(\mathbb{R}^n)$ for ${n-1\over 2n}\leq {1\over p}\leq{n+1\over 2n}$.