Regularity of Fourier integral operators with amplitudes in general Hörmander classes
Castro A.J. Israelsson A. Staubach W.
September 2021Birkhauser
Analysis and Mathematical Physics
2021#11Issue 3
We prove the global Lp-boundedness of Fourier integral operators that model the parametrices for hyperbolic partial differential equations, with amplitudes in classical Hörmander classes Sρ,δm(Rn) for parameters 0 ≤ ρ≤ 1 , 0 ≤ δ< 1. We also consider the regularity of operators with amplitudes in the exotic class S0,δm(Rn), 0 ≤ δ< 1 and the forbidden class Sρ,1m(Rn), 0 ≤ ρ≤ 1. Furthermore we show that despite the failure of the L2-boundedness of operators with amplitudes in the forbidden class S1,10(Rn), the operators in question are bounded on Sobolev spaces Hs(Rn) with s> 0. This result extends those of Y. Meyer and E. M. Stein to the setting of Fourier integral operators.
Fourier integral operators , Hyperbolic PDEs , Hörmander classes
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Department of Mathematics, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan
Department of Mathematics, Uppsala University, Uppsala, S-751 06, Sweden
Department of Mathematics
Department of Mathematics
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