  In this paper we give an elementary proof for transference of local to global
maximal estimates for dispersive PDEs. This is done by transferring local $L^2$
estimates for certain oscillatory integrals with rough phase functions, to the
corresponding global estimates. The elementary feature of our approach is that
it entirely avoids the use of the wave packet techniques which are quite common
in this context, and instead is based on scalings and classical oscillatory
integral estimates.
