Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 083-01. A uniform Hilbert transform estimate for Lipschitz directions
Manuscript map · lines 4095–4104
OpenAI@2026-10-07#rem:oai-p-083-01
Authors: OpenAI. Family 083.
Title: A uniform Hilbert transform estimate for Lipschitz directions.
Abstract: We prove a uniform L2 bound for the Hilbert transform along a Lipschitz unit vector field in the plane, with integration restricted to a fixed absolute multiple of the reciprocal Lipschitz seminorm. The bound is uniform in the inner truncation and holds for fields depending on both coordinates. This gives an affirmative answer to Stein's weak-$(2,2)$ conjecture.
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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