变量各向异性的非齐次拟微分象征类

Variable Anisotropic Class of Inhomogeneous Pseudo-differential Symbols

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)).