{"id":"openai-math/Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere","pdf":"https://github.com/openai/math/blob/main/preprints/Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere-September-24-2026/Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere-September-24-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Elliptic-capacity-propagation-and-Fourier-restriction-to-the-sphere-September-24-2026","tags":["harmonic-analysis","fourier-restriction","geometric-analysis"],"score":0,"title":"Elliptic capacity propagation and Fourier restriction to the sphere","domain":"Real and complex analysis","family":"077","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.CA","summary":"We prove the bounded-data Fourier restriction conjecture for the sphere in three dimensions: the Fourier extension operator maps $`L^\\infty(S^2)`$ boundedly into $`L^p(\\mathbb R^3)`$ for every p > 3. This is the full conjectured open range, and the threshold p = 3 is sharp.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":false,"family_title":"Fourier restriction for positively curved surfaces"}