调和Bergman空间上弱局部化算子的代数

Algebra of the weakly localized operators on harmonic Bergman spaces

本文在Rn中开单位球的调和Bergman空间bp上引入一类(p,δ)-弱局部化算子,这类算子构成一个代数并包含了bp上的Toeplitz代数.本文的主要结果还给出这类算子的一个紧性判据,即T为bp上的紧算子当且仅当存在k>0,使得lim sup|x|→1-supy∈D(x,k)|<T r(p)y,r(p′)x>|=0.

In this note, we introduce a class of the so-called weakly localized operators on the harmonic Bergman spaces, which forms an algebra and contains all Toeplitz operators with bounded symbols. Our main result gives a criterion of the compactness for this class of operators, i.e., T is a compact operator on bpif and only if there exists k 0, such that lim sup｜x｜→1-supy∈D（x,k）｜T r（p）y, r（p′）x｜ = 0.