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| The Hp-Hq Estimates for a Class ofDispersive Equations with Finite TypeGeometry |
| Qingquan Deng,Xuejian Meng |
| (School of Mathematics and Statistics and Key Laboratory of Nonlinear
Analysis & Applications (Ministry of Education), Central China Normal
University, Wuhan, Hubei 430079, China;School of Mathematics and Statistics, and Hubei Key Laboratory of
Mathematical Sciences, Central China Normal University, Wuhan,
Hubei 430079, China) |
| DOI： |
| Abstract: |
| This paper studies the Hp?Hq
estimates of a class of oscillatory
integrals related to dispersive equations
(
i?tu(t,x)=Q(D)u(t,x), (t,x)∈R×R
n
,
u(0,x)=u0(x), x∈R
n
,
under the assumption that the level hypersurfaces are convex and of finite type.
As applications, we obtain the decay estimates for the solutions of higher order
homogeneous and inhomogeneous Schr¨odinger equations. |
| Key words: Dispersive equations, Hp−Hq
estimates, finite type geometry, decay estimates. |