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The three-dimensional Bochner–Riesz conjecture

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\}

Manuscripts in this family · 1

Bochner–Riesz multipliers in three dimensions

Sep 24, 2026·Bochner-Riesz-Multipliers-in-Three-Dimensions-September-24-2026.pdf

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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