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

作　　者：Ing-Lung HWANG 

机构地区：[1]Department of Mathematics,“National Chung Cheng University of Taiwan”,Chiayi County 621003,China

出　　处：《Acta Mathematica Sinica,English Series》2023年第1期37-98,共62页数学学报（英文版）

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≤∞,k>n/2,k’>0 respectively).Suppose the phase function S is positively homogeneous inξ-variables,non-degenerate and satisfies certain conditions.Then the Fourier integral operator T is L^(p)-bounded.Applying 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≤δ<1 and k,k’given as in(1),then the L^(p)-boundedness of the pseudo-differential operators holds,1<p<∞.

关 键 词：Fourier integral operator L^(p)-boundedness 

分 类 号：O177[理学—数学]