  We prove uniform estimates for the decay rate of the Fourier transform of
measures supported on real-analytic hypersurfaces in R^3. If the surface
contains the origin and is oriented such that its normal at the origin is in
the direction of the z-axis and if dS denotes the surface measure for this
surface, then the measures under consideration are of the form K(x,y)g(z) dS
where K(x,y)g(z) is supported near the origin and both K(x,y) and g(z) are
allowed to have singularities. The estimates here generalize the previously
known sharp uniform estimates for when K(x,y)g(z) is smooth. The methods used
in this paper involve an explicit two-dimensional resolution of singularities
theorem, iterated twice, coupled with Van der Corput-type lemmas.
