加权Bergman空间上Carleson测度

Carleson measures on the weighted Bergman spaces

讨论带正规权的加权Bergman空间 Ap() 上的 Carleson型测度,若μ为复平面单位圆盘上的非负Borel测度,证明了μ为 Ap() 上的消没 Carleson测度的充要条件是μ在伪双曲圆盘 D(z,r) 上的平均当| z |→1- 时趋向于0.

The present paper investigates the Carleson-type measures on the weighted Bergman spaces A^p() with a normal weight. If μ is a nonnegative Borel measure on the unit disk in the complex plane, it was showed that μ is a vanishing Carleson measure on A^p() if and only if the average of μ on the pseudo-hyperbolic disks D(z,r) tends to 0 as |z|→1^-.