Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 082-01. Annular variation of the triangular Hilbert transform at the symmetric point
Manuscript map · lines 4065–4074
OpenAI@2026-10-07#rem:oai-p-082-01
Authors: OpenAI. Family 082.
Title: Annular variation of the triangular Hilbert transform at the symmetric point.
Abstract: We prove the annular r-variation estimate for the triangular Hilbert transform from complex $L{}3{}times L{}3$ to L3/2 for every r > 2. The partitions may depend on the output point and range over all positive scales. The estimate yields the two-endpoint maximal bound and joint almost-everywhere and norm principal values, and resolves the symmetric scalar triangular Hilbert transform problem.
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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