Decomposition Theorems and Conjugate Pair in D_K Spaces  

作　　者：Ji Zhen ZHOU Yu Tian WU 

机构地区：[1]School of Sciences,Anhui University of Science and Technology [2]School of Mathematics and Information Sciences,Zhaoqing University

出　　处：《Acta Mathematica Sinica,English Series》2014年第9期1513-1525,共13页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China(Grant No.11071153);the first author is supportby Department of Education of Anhui Province(Grant No.KJ2013A101);the second author is supported by National Natural Science Foundation of China(Tianyuan fund for Mathematics,Grant No.11226182);the Scientific Research Fund of Zhaoqing University(201209)

摘　　要：Let K be a right-continuous and nondecreasing function. A function f analytic in the unit disk D belongs to the space OK if ∫D｜f＇（z）｜2K（1 - ｜z｜2）dA（z） 〈 ∞. Decomposition theorems for OK spaces are established in this paper. As an application, we obtain a characterization of interpolation by functions in DK spaces. Furthermore, we characterize functions in DK spaces by conjugate pairs.Let K be a right-continuous and nondecreasing function. A function f analytic in the unit disk D belongs to the space OK if ∫D｜f＇（z）｜2K（1 - ｜z｜2）dA（z） 〈 ∞. Decomposition theorems for OK spaces are established in this paper. As an application, we obtain a characterization of interpolation by functions in DK spaces. Furthermore, we characterize functions in DK spaces by conjugate pairs.

关 键 词：DK spaces decomposition theorem conjugate pair 

分 类 号：O177[理学—数学]