加权Bergman空间上的Rudin正交性问题

Rudin Orthogonality Problem on the Weighted Bergman Space

通过构造广义计数函数N（φ）,α（w）,研究了加权Bergman空间A2a（D）上的Rudin正交性问题.证明了（φ）：D→D解析,（φ）（0）=0时,{（φ）k：k=0,1,2,…}构成加权Bergman空间Aα2（D）的正交集当且仅当函数Nφ（φ）α（w）=∑（φ）（z）∞∑n=1（1-｜z｜2）n＋α＋1是本性径向的;当解析函数（φ）为n阶有限Blaschke乘积且（φ）（0）=0时,若存在正整数N使得∑｜ z ｜ 2N/φ（φ）α（w）是本性径向的,则（φ）=czn,其中c为常数.

In this paper, The writers study Rudin orthogonality problem on the weighted Bergman space A2a（D） by constructing a generalized Nevanlinna counting function Nφ（φ）α（w）, and show that if a self-map φ： D→Dis analytic withφ（O） = O, then the set {（φ）k：k=0,1,2,…} is orthogonal in A2a（D） if and only if Nφ（φ）α（w） is essentially radial, and show that when φ is a finite Blaschke product with order n, and φ（O） = O, if there exits a positive integer N subjecting the function ∑｜ z ｜ 2N/φ（φ）α（w） to be essentially radial, then , φ）=czn where c is some constant.