  We obtain optimal continuity in Sobolev spaces for the Fourier integral
operators associated to singular canonical relations, when one of the two
projections is a Whitney fold. The regularity depends on the type, $k$, of the
other projection from the canonical relation ($k=1$ for a Whitney fold). We
prove that one loses $(4+\frac{2}{k})^{-1}$ of a derivative in the regularity
properties.
  The proof is based on the $L^2$ estimates for oscillatory integral operators.
