The Bochner–Riesz Problem: An Old Approach Revisited

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.

Keywords

Bochner–Riesz operator / Polynomial method / Restriction problem

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Peking University