Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 082-03. The maximal triangular Hilbert transform at the symmetric point
Manuscript map · lines 4085–4094
OpenAI@2026-10-07#rem:oai-p-082-03
Authors: OpenAI. Family 082.
Title: The maximal triangular Hilbert transform at the symmetric point.
Abstract: For arbitrary complex inputs in $L{}3({}mathbb R{}2)$, we prove the pointwise maximal $L{}3{}times L{}3{}to L{}{3/2}$ estimate for the triangular Hilbert transform, with the supremum over both hard truncation endpoints. The estimate yields joint almost-everywhere and L3/2 convergence as the lower endpoint tends to zero and the upper endpoint tends to infinity. This also proves the conjectured scalar estimate at the symmetric point.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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