Let $X$ be a complex manifold, let $\Omega \subset X$ be a domain with smooth boundary $M=\partial\Omega$, and regard $M$ as a smooth real hypersurface with its induced CR structure $T^{0,1}M \subset T^{0,1}X|_M$. If $U \subset X$ is an open neighbourhood of $M$, if $F:U\to\mathbb C$ is holomorphic, and if $u:M\to\mathbb C$ is the restriction $u=F|_M$, then $u$ is a CR function on $M$; equivalently,

\begin{align*} \bar\partial_b u=0. \end{align*}