Properties Of Hankel Type Operators Restricted To Weighted Harmonic Bergman Spaces

Hankel operators have been studied by many scholars,some very important results have been achieved.This paper studies Hankel type operators restricted to weighted harmonic Bergman spaces,and obtains some properties of Hankel type operators.The main results and innovation points are as follows:1.Introduced the definition and basic properties of the weighted harmonic Bergman space and Hankel type operators;2.Using the orthonormal basis of weighted harmonic Bergman spaces,we proved that Hankel type operators S1 and S1 are Hilbert-Schmidt operators.Furthermore,for a finite degree polynomial p(z)on the unit disk D,by using the orthonormal basis we proved that Hankel type operators H/p(z)and Hp(z)are Hilbert-Schmidt operators on the weighted harmonic Bergman space;3.Given a harmonic(n,n)-form F,we obtained the integral representations of har-monic(n,n-1)-form u1 and harmonic(n-1,n)-form u2 such that(?)u1+(?)u2=F.