六盘水师范学院学报2026，Vol.38Issue(1)：62-77,16.DOI:10.16595/j.1671-055X.2026.01.006
加权Bers空间中具有Hadamard间隙的解析函数
Analytic Functions with Hadamard Gaps on the Weighted Bers Space
摘要
Abstract
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.关键词
Hadamard间隙/加权Bers空间/解析函数/有界性Key words
Hadamard gaps/Weighted Bers space/Analytic function/Boundedness分类
数理科学引用本文复制引用
张应琴,杨丛丽,罗玲..加权Bers空间中具有Hadamard间隙的解析函数[J].六盘水师范学院学报,2026,38(1):62-77,16.基金项目
国家自然科学基金项目"对数凹函数集的几何理论研究"(12361011). （12361011）
