Global estimates of fundamental solutions for higher-order Schrödinger equations
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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 L p –L q estimates on the Schrödinger solution. These estimates extend known results from the literature and are sharp. This result was lately already generalized to a degenerate case (cf. ).
KeywordsOscillatory integral Higher-order Schrödinger equation Fundamental solution estimate
Mathematics Subject Classification (2000)42B20 42B37 35Q41 35B65
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