Resolves the three-dimensional Bochner–Riesz conjecture in its strict range: the Bochner–Riesz multipliers of order δ are bounded on L^p(\mathbb R^3) for every 1\le p\le\infty whenever \delta\gt \max\{3|1/p-1/2|-1/2,0\}.
Manuscript
Bochner–Riesz multipliers in three dimensions
September 24, 2026 · source · cite as \cite{OAI:Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026}
We prove the three-dimensional Bochner–Riesz conjecture in its strict-order formulation. The main result is boundedness of the Bochner–Riesz multipliers on L^3(\mathbb R^3) for every positive order. Interpolation and duality then give the full conjectured strict range.
Result 078 · Real and complex analysis. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md