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  "body": "\n## Summary\n\nA CR function on a [[CR manifold|ZC78JKZX9S]] is a function annihilated by the anti-holomorphic tangent vectors of the CR structure, see the [[definition|Z23FCT4WTZ]].\nOn a real hypersurface of $\\C^n$, these are the solutions of the [[tangential Cauchy–Riemann equations|X7GP9BECD8]], and the restriction of any holomorphic function is one.\nThe [[Lewy extension theorem|V2YCGHD719]] shows that on a strongly pseudoconvex hypersurface, CR functions extend locally holomorphically to one side.\nSo they are locally boundary values of holomorphic functions.\n\n## Explanations\n\n### L1 human\n\nOn a surface in $\\C^n$ one cannot ask a function to be holomorphic, since the surface is not a complex space.\nOne can still ask it to satisfy the Cauchy–Riemann equations in the directions that the surface allows.\nThese are the CR functions.\nRestrictions of holomorphic functions are the main examples, and in good cases every CR function is of this kind.\n",
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