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- Title
L<sup>2</sup> Boundedness of the Fourier Integral Operator with Inhomogeneous Phase Functions.
- Authors
Dai, Jia Wei; Chen, Jie Cheng
- Abstract
In this paper, we investigate the L2 boundedness of the Fourier integral operator Tø,a with smooth and rough symbols and phase functions which satisfy certain non-degeneracy conditions. In particular, if the symbol a ∈ L ∞ S ρ m , the phase function ø satisfies some measure conditions and ∥ ∇ ξ k ϕ (⋅ , ξ) ∥ L ∞ ≤ C ∣ ξ ∣ ϵ − k for all k ≥ 2,ξ ≠ 0, and some ϵ > 0, we obtain that Tø,a is bounded on L2 if m < n 2 min { ρ − 1 , − ϵ 2 } . This result is a generalization of a result of Kenig and Staubach on pseudo-differential operators and it improves a result of Dos Santos Ferreira and Staubach on Fourier integral operators. Moreover, the Fourier integral operator with rough symbols and inhomogeneous phase functions we study in this paper can be used to obtain the almost everywhere convergence of the fractional Schrödinger operator.
- Subjects
FOURIER integrals; PSEUDODIFFERENTIAL operators; SCHRODINGER operator; INTEGRAL operators
- Publication
Acta Mathematica Sinica, 2023, Vol 39, Issue 8, p1525
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-023-2149-z