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# Oscillatory integrals with nonhomogeneous phase functions related to Schrödinger equations

Published:1998-09-01
Printed: Sep 1998
• Lawrence A. Kolasa
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## Abstract

In this paper we consider solutions to the free Schr\" odinger equation in $n+1$ dimensions. When we restrict the last variable to be a smooth function of the first $n$ variables we find that the solution, so restricted, is locally in $L^2$, when the initial data is in an appropriate Sobolev space.
 MSC Classifications: 42A25 - unknown classification 42A2542B25 - Maximal functions, Littlewood-Paley theory