The Weakly Localized Operators In Weighted Harmonic Bergman Space L_h~p(D,dA_?)

In this article,we introduce the notion of the weakly localized operators on the weighted harmonic Bergman space which forms an algebra and contains all Toeplitz operators with bounded symbols.Our main result gives a criterion of the compactness of this kind of operators.In the analytic Bergman space Lap,as we all known,the operator's compactness can be characterized by its berezin transform.In this note,we get a similar result:suppose 1<p<?,T is a compact operator on Hp(D)if and only if T belongs to the norm closure of Hp(D),and (?)...