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.
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)
