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Oscillatory integrals with nonhomogeneous phase functions related to Schrödinger equations

Open Access article
 Printed: Sep 1998
  • Lawrence A. Kolasa
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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, 42B25 show english descriptions unknown classification 42A25
Maximal functions, Littlewood-Paley theory
42A25 - unknown classification 42A25
42B25 - Maximal functions, Littlewood-Paley theory

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