OpenAI · 086-01 · 2026-10-05 · Real and complex analysis

An L^3 bound for the trilinear Hilbert transform

preprints/An-L3-bound-for-the-trilinear-Hilbert-transform-October-5-2026

Family 086. An $L^{3}$ bound for the trilinear Hilbert transform.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N

Proves that the principal-value trilinear Hilbert transform with shifts $x - t$ , $x - 2 t$ , $x - 3 t$ is bounded from $L^{3} (R)^{3}$ to $L^{1} (R)$ . This resolves the $L^{3}$ exponent case of the standard conjecture for slopes $1, 2, 3$ .

We prove that the trilinear Hilbert transform with fixed slopes 1, 2, 3 maps $L^{3} (R) \times L^{3} (R) \times L^{3} (R)$ to $L^{1} (R)$ , resolving this case of the trilinear Hilbert transform conjecture.

Preprint source and Lean scope

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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.