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- Title
Fourier integral operators with forbidden symbols on the Besov spaces.
- Authors
Ruan, Jianmiao; Zhu, Xiangrong
- Abstract
In this note, we consider the Fourier integral operator T ϕ , a f (x) = ∫ R n e i ϕ (x , ξ) a (x , ξ) f ^ (ξ) d ξ with 푎 in the forbidden Hörmander class S ρ , 1 m and ϕ ∈ Φ 2 satisfying the strong non-degeneracy condition. For 0 ≤ ρ ≤ 1 , set m (n , ρ , p) = − (n − ρ) (1 2 − 1 p) + n p (ρ − 1) . When 2 ≤ p ≤ ∞ , 1 ≤ q ≤ ∞ and s > m − m (n , ρ , p) , we show that T ϕ , a is bounded from the Besov space B p , q s to B p , q s − m + m (n , ρ , p) . This result is a generalization of some theorems proved by Stein, Meyer, Runst and Bourdaud for the pseudo-differential operator T a with a ∈ S 1 , 1 m , and indices 푠 and m (n , ρ , p) are sharp in some cases.
- Subjects
BESOV spaces; FOURIER integrals; PSEUDODIFFERENTIAL operators; SIGNS &; symbols
- Publication
Forum Mathematicum, 2024, Vol 36, Issue 2, p417
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2023-0092