加权Bers空间中具有Hadamard间隙的解析函数OA

By using a positive continuous function ω on(0,1],the weighted Bers space ℋ∞α,ω and the little weighted Bers space ℋ∞α,ω,0 are defined.The necessary and sufficient conditions for an analytic function with Hadamard gaps on the unit open disk to belong to these two spaces are characterized.By us-ing the conclusion that f(x)∈ℋ∞α,ω if and only if supn-αk|ank|/ω(1/nk)=0 as k→ ∞,it is proved that there exist two different functions f1(x)and f2(x)in the Bers space ℋ∞α,and the sum of their moduli has a lower bound,that is,|f1(z)|+|f2(z)|≥C/(1-|z|)α.The value of this paper is that,without constructing test func-tions,by using this lower bound,the necessary and sufficient conditions for the boundedness of the weight-ed composition operator from the Bers space ℋ∞α to the Bers space ℋ∞β on the unit disk are obtained.