一类拟微分算子的加权Morrey不等式

Weighted Morrey Inequality for a Class of Pseudo-differential Operators

该文研究了一类象征a(x,ξ)属于L∞Sρ^m(R^n),ρ≤1的拟微分算子在加权Morrey空间Lω^p,κ(R^n)上的有界性问题,其中ω为Ap权.类似Kening和Staubach证明其Lp有界性的方法,该文获得了当q≥p时,如果m和p满足一定的条件,则拟微分算子在加权Morrey空间Lω^q,κ(R^n)上有界。

In this paper,we study some sufficient conditions for the boundedness of a class of pseudo-differential operators T with symbols a(x,ξ)∈L∞ Sρ^m(R^n) and ρ≤1 on weighted Morrey spaces Lω^p,k(R^n),where ω∈A p.Namely,under some conditions of m and p,the pseudo-differential operators T are bounded on weighted Morrey spaces Lω^q,κ(R^n)for q≥p.Our proof follows Kening and Staubach’s method on L^p boundedness.