Sharp Lp-boundedness of oscillatory integral operators with polynomial phases

In this paper, we shall prove the L-p endpoint decay estimates of oscillatory integral operators with homogeneous polynomial phases S in R x R. As a consequence, sharp Lp decay estimates are also obtained when polynomial phases have the form S( x(m1), y(m2)) with m(1) and m(2) being positive integers. In this paper, we shall prove the endpoint decay estimates of oscillatory integral operators with homogeneous polynomial phases S in . As a consequence, sharp decay estimates are also obtained when polynomial phases have the form with and being positive integers.