A maximal Fourier integral operator and an application

Abstract

In this note we establish a strong type \(L^2\) inequality for a maximal Fourier integral operator, generalizing a related result of Rubio de Francia (Duke Math J 53:395–404, 1986). As an application, we also give an alternative proof of Sogge’s theorem (Fourier integrals in classical analysis, Cambridge University press, Cambridge, 1993) on the boundedness of the spherical maximal operator on the \(n\)-sphere, whenever \(p>n/(n-1)\) and \(n\ge 3 \).