  In this paper we consider estimate for oscillatory integrals with stationary
phase. First, we consider the uniform stationary estimate which was previously
studied by Alazard, Burq, and Zuily and significantly improve the regularity
requirement for the phase and amplitude functions. Secondly, we also consider
estimate for oscillatory integral of which phase and amplitude depend on the
oscillation parameter. Novelty of this article lies in theuse of wave packet
decomposition, which turns decay estimate for oscillatory integral into
disjointness property of the supports of wave packets. The latter is geometric
in its nature and less sensitive to smoothness of the phase and amplitude
functions and this enables us to obtain uniform stationary phase estimate under
weaker regularity assumption.
