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Sharp maximal estimates for doubly oscillatory integrals

Authors:	Bjö rn Gabriel Walther

Affiliation:	Department of Mathematics, Royal Institute of Technology, SE -- 100 44 Stockholm, Sweden

Abstract:	We study doubly oscillatory integrals $begin{displaymath}int_{mathbf R^n} , e^{i(xi + yvertxivert + tvertxivert^ a)} widehat f(xi),dxi end{displaymath}$ and prove a sharp maximal estimate which is an immediate consequence of a well-known conjecture in Fourier analysis on $mathbf{R}^n$ .

Keywords:	Doubly oscillatory Fourier integrals, maximal estimates, wave equation, time-dependent Schr" odinger equation

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