Lp boundedness of Fourier integral operators with rough symbols

Abstract

In this note we consider Fourier integral operators Tϕ,a with rough symbols which behave in the spatial variable like an L∞ function. Assuming certain weak condition on the phase function we get an L∞-boundedness result of Tϕ,a, which generalizes an earlier result of Kenig and Staubach on pseudo-differential operators. We also prove two boundedness results of Tϕ,a on L∞ and Lp, which improve some results of Dos Santos Ferreira and Staubach on Fourier integral operators.