  We investigate analyticity properties of correlation functions in conformal
field theories (CFT) in the Wightman formulation. The goal is to determine
domain of holomorphy of permuted Wightman functions. We focus on crossing
property of three-point functions. The domain of holomorphy of a pair of
three-point functions is determined by appealing to Jost's theorem and by
adopting the technique of analytic completion. This program paves the way to
address the issue of crossing for the four-point functions on a rigorous
footing.
