消失Bergman-Carleson测度和小Bloch空间的特征(英文)

Characterizations of Vanishing Bergman-Carleson Measure and Little Bloch Space

本文给出了消失Ｂｅｒｇｍａｎ－Ｃａｒｌｅｓｏｎ测度的一个特征，证明了：当ｆ∈Ｈ（Ｂ），０＜ｐ＜∞时，ｆ∈Ｂ０等价于ｌｉｍ｜ｚ｜→１｜Δｆ（ｚ）｜＝０，等价于ｌｉｍ｜ａ｜→１∫Ｂ｜Δｆ（ｚ）｜ｐＪＲφａ（ｚ）ｄｖ（ｚ）＝０，等价于Δｆ（ｚ）｜ｐｄｖ（ｚ）是消失Ｂｅｒｇｍａｎ－Ｃａｒｌｅｓｏｎ测度．

In this paper, a characterization of vanishing Bergman-Carleson measure is given and it is proved that for f∈H(B), 0<p<∞ , f∈B 0 if and only if lim |z|→1 | Δ ～ f(z)|=0 , if and only if lim |a|→1 ∫ B| Δ ～f(z)| pJ Rφa(z)dv(z)=0 , if and only if | Δ ～ f(z)| pd v(z) is a vanishing Bergman-Carleson measure.