L^(p)Boundedness of Fourier Integral Operators in the Class S_(1,0)

作     者：Ing-Lung HWANG Ing-Lung HWANG

作者机构：Department of Mathematics“National Chung Cheng University of Taiwan”Chiayi County 621003China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2023年第39卷第1期

页      面：37-98页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Fourier integral operator L^(p)-boundedness 

摘      要：We prove the following properties:(1)Let a∈Λ_(1,0,k,k’)^(m0)(R^(n)×R^(n))with m0=-1|1/p-1/2|(n-1),n≥2(1 n/p,k’0;2≤p≤∞,kn/2,k’0 respectively).Suppose the phase function S is positively homogeneous inξ-variables,non-degenerate and satisfies certain *** the Fourier integral operator T is L^(p)-*** the method of(1),we can obtain the L^(p)-boundedness of the Fourier integral operator if(2)the symbol a∈Λ_(1,δ,k,k’)^(m0),0≤δ≤1,with m0,k,k’and S given as in(1).Also,the method of(1)gives:(3)a∈Λ_(1,δ,k,k’),0≤δ1 and k,k’given as in(1),then the L^(p)-boundedness of the pseudo-differential operators holds,1p∞.