The Bochner-Riesz problem: an old approach revisited

TL;DR

This paper applies recent Fourier restriction techniques to the Bochner-Riesz problem, using pseudo-conformal transformations and induction-on-scales, leading to improved results matching the best known Fourier restriction ranges in high dimensions.

Contribution

It introduces a novel approach by adapting Fourier restriction methods to the Bochner-Riesz problem, achieving the best known results in high dimensions.

Findings

Improved the Bochner-Riesz problem to the best known Fourier restriction range in high dimensions.

Applied pseudo-conformal transformation and induction-on-scales techniques.

Unified approach enhances understanding of Fourier analysis problems.

Abstract

We show that the recent techniques developed to study the Fourier restriction problem apply equally well to the Bochner-Riesz problem. This is achieved via applying a pseudo-conformal transformation and a two-parameter induction-on-scales argument. As a consequence, we improve the Bochner-Riesz problem to the best known range of the Fourier restriction problem in all high dimensions.