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 $\delta\gt \max\{3|1/p-1/2|-1/2,0\}$.
released 2026-09-24 | 8 theorems · 27 lemmas · 44 proofs · 53,838 words |
PLAY LEVEL 1 »(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.