α-正规函数的一些积分准则

Some Integral Criteria forα-Normal Functions

对0〈α〈∞,N^α是开单位圆盘D上满足sup（1-｜z｜^2）^αf^#（z）〈∞的亚纯函数类,其中,f^#（z）=｜f′｜（z）｜/（1＋｜f（z）｜^2）是,的球面导数.该文给出了D上的α-正规函数类的—些积分准则,并用Bergman-Carleson测度的形式予以表示.

For 0 〈 α 〈 ∞, N^α is the class of meromorphic functions f defined in the unit disk D satisfying sup（1 -｜z｜^2）^αf^#（z） 〈 ∞, where f^#（z） = ｜f＇（z）｜/（1 ＋ ｜f（z）｜^2）. Some new characterizations of the a-normal functions are given for 0 〈 α 〈 1. Characterizations are given in terms of the Bergman-Carleson measure conditions and the compact Bergman-Carleson conditions.