On 𝐿𝑝 boundedness of rough Fourier integral operators

Author:

Wu Guoning1,Yang Jie1

Affiliation:

1. College of Mathematics and System Science , 47907 Xinjiang University , Xinjiang 830046 , P. R. China

Abstract

Abstract In this paper, we deal with the L p L^{p} boundedness of rough Fourier integral operators T a , φ T_{a,\varphi} with amplitude a ( x , ξ ) L S ρ m a(x,\xi)\in L^{\infty}S_{\rho}^{m} and phase function φ ( x , ξ ) L Φ 2 \varphi(x,\xi)\in{L^{\infty}}{\Phi^{2}} which satisfies a measure condition. We show that T a , φ T_{a,\varphi} is bounded on L p L^{p} for 1 p 1\leq p\leq\infty if m < n ( ρ 1 ) p ρ ( n 1 ) 2 p m<\frac{n(\rho-1)}{p}-\frac{\rho(n-1)}{2p} when 1 p 2 1\leq p\leq 2 or m < n ( ρ 1 ) 2 ρ ( n 1 ) 2 ( 1 1 p ) m<\frac{n(\rho-1)}{2}-\frac{\rho(n-1)}{2}(1-\frac{1}{p}) when 2 p 2\leq p\leq\infty . Our main results extend and improve some known results about L p L^{p} boundedness of Fourier integral operators.

Funder

Natural Science Foundation of Xinjiang Province

National Natural Science Foundation of China

Publisher

Walter de Gruyter GmbH

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