CR function

Summary

A CR function on a CR manifold is a function annihilated by the anti-holomorphic tangent vectors of the CR structure, see the definition. On a real hypersurface of $\C^n$, these are the solutions of the tangential Cauchy–Riemann equations, and the restriction of any holomorphic function is one. The Lewy extension theorem shows that on a strongly pseudoconvex hypersurface, CR functions extend locally holomorphically to one side. So they are locally boundary values of holomorphic functions.