{"id":"openai-math/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point","pdf":"https://github.com/openai/math/blob/main/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026/annular-variation.pdf","url":"https://github.com/openai/math/tree/main/preprints/Annular-variation-of-the-triangular-Hilbert-transform-at-the-symmetric-point-October-5-2026","tags":["harmonic-analysis","triangular-hilbert-transform"],"score":0,"title":"Annular variation of the triangular Hilbert transform at the symmetric point","domain":"Real and complex analysis","family":"082","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We prove the annular r -variation estimate for the triangular Hilbert transform from complex $`L^3\\times L^3`$ to L 3/2 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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Annular variation and dyadic absolute bounds for the triangular Hilbert transform"}