∑math20

Real and complex analysis · Result 078

The three-dimensional Bochner–Riesz conjecture

1 paper

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 \(\delta\gt \max\{3|1/p-1/2|-1/2,0\}\).

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▶Introduction: the problem and why it mattersin preparation
▶The presented solutionin preparation

Papers 1

First page of Bochner–Riesz multipliers in three dimensions

Bochner–Riesz multipliers in three dimensions

OpenAI · 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.

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@misc{OAI:Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026,
  author = {{OpenAI}},
  title = {{Bochner--Riesz multipliers in three dimensions}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026/Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026.pdf}{OAI:Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.