  A local two-dimensional resolution of singularities theorem and arguments
based on the Van der Corput lemma are used to give new estimates for the decay
rate of the Fourier transform of a locally defined smooth hypersurface measure
in R^3, as well as to provide new proofs of some known estimates. These are
then used to give L^q bounds on solutions to certain PDE problems in terms of
the L^p norms of their initial data for various values of p and q.
  Unlike much of the earlier work in this subject, no use is made of the
adapted coordinate systems that have been often been used to study
two-dimensional oscillatory integrals; all of the needed information is
furnished by the resolution of singularities theorem.
