The Boundedness And Compactness Of Generalized Area Operators From H~p To L~q

In this paper,we study mainly the positive measuresμon the unit disk, necessary conditions and sufficient conditions are given for it making the area operators A_μfrom Hardy spaces H~p to L~q(T) to be bounded or compact.Our mian results are as follows.1.necessary conditions and sufficient conditions are given forμmaking the area operators A_μfrom H~p to L~q(T) to be bounded.2.necessary conditions and sufficient conditions are given forμmaking the area operators A_μfrom H~p to L~q(T) to be compact.