变量各向异性的非齐次拟微分象征类  

Variable Anisotropic Class of Inhomogeneous Pseudo-differential Symbols

作　　者：杨娅娟 余安康 李宝德[1] Ya Juan YANG;An Kang YU;Bao De LI(College of Mathematics and System Sciences,Xinjiang University,Urumqi 830046,P.R.China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《数学学报（中文版）》2021年第5期747-760,共14页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11861062);新疆创新环境(人才、基地)建设专项—自然科学计划(自然科学基金)联合基金(2020D01C048)。

摘　　要：设θ_(0)是R^(n)上的连续多尺度椭球覆盖Θ的中心正则子覆盖.本文引入了一类适应于椭球子覆盖θ_(0)的非齐次拟微分象征类S_(δ,δ)0(θ_(0)),0≤δ<1.此象征类推广了经典的各向齐性非齐次象征类S_(δ,δ)0(I_(n)),其中I_(n)是n×n的单位矩阵.然后本文将一个经典的L^(2)(R^(n))有界性结果推广到了此象征类S_(δ,δ)0(θ_(0))的情形下.Letθ_(0)be a central regular ellipsoid subcover of a continuous multi-level ellipsoid coverΘof Rn.We introduce a class of inhomogeneous pseudo-differential symbols S^(δ),δ_(0)(θ0)adapted to 0,which generalizes the classical isotropic inhomogeneous class S_(δ,δ)^(0)(In),where 0≤δ<1 and In is an identity n×n matrix.We extend a well-known L^(2)(R^(n))-boundedness result to the variable anisotropic inhomogeneous class S_(δ,δ)^(0)(θ_(0)).

关 键 词：拟微分算子 各向异性 有界性 椭球 

分 类 号：O174.2[理学—数学]