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

Text of the article Перейти на текст статьи

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

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026