Bloch型函数的高阶径向导数(英文)

Higher Order Radial Derivatives of Bloch Type Functions

讨论了复超球上全纯函数的高阶导数的增长速度 ,证明了f∈Bα 的充分必要条件是supa∈B(1- ｜z｜2 ) m+α- 1｜Rmf(z) ｜ <∞ ,或supa∈B∫B(1-｜z｜2 ) (m+α- 1) ｜Rmf(z) ｜pJRφα(z)dv(z) <∞ ,或 (1- ｜z｜2 ) p(m+α- 1) ｜Rmf(z) ｜pdv(z)是Bergman Carleson测度 .

In this paper, higher order radial derivatives of Bloch type functions in the unit ball of C n is discussed and it is proved that for f∈H(B), f∈ B α if and only if sup α∈B(1-|z| 2) m+α-1 |R mf(z)|<∞, if and only if  sup a∈B∫ B(1-|z| 2) P(m+α-1) |R mf(z)| PJ Rφ α(z) d v(z)<∞, if and only if (1-|z| 2) P(m+α-1) |R mf(z)| P d v(z) is a Bergman Carleson measure.