Global estimates of fundamental solutions for higher-order Schrödinger equations

Abstract

In this paper we first establish global pointwise time-space estimates of the fundamental solution for Schrödinger equations, where the symbol of the spatial operator is a real non-degenerate elliptic polynomial. Then we use such estimates to establish related Lp-Lq estimates on the Schrödinger solution. These estimates extend known results from the literature and are sharp. This result was latetly already generalized to a degenerate case (cf. [9]).

References in corpus (1)

• Convex Hypersurfaces and $L^p$ Estimates for Schrödinger Equations

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• Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit, II