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Sharp maximal estimates for doubly oscillatory integrals

Authors:	Bjö rn Gabriel Walther

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

Abstract:	We study doubly oscillatory integrals $\begin{displaymath}\int_{\mathbf R^n} \, e^{i(\xi + y\vert\xi\vert + t\vert\xi\vert^ a)} \widehat f(\xi)\,d\xi \end{displaymath}$ 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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