加权Bergman空间到Bloch型空间的广义Cesàro算子(英文)

From Weighted Bergman Spaces to the Broad Sense Bloch Cesàro

给定单位球B上的解析函数g,刻划了从加权Bergman空间到Bloch型空间及小Bloch型空间的广义Cesàro算子Lg的有界性和紧性特征.此处Lg定义为Lgf(z) =∫10g(tz)f(tz)dt/t.

We characterize the boundary and compactness of the extended Cesàro operator Lg from the weighted Bergman space Aa^p（φ） to Bloch - type space βμ, where g is a given holomorphic function in the unit ball of C^n,φ,μ are both normal functions and Lg is defined by Lgf（z） =∫0^1g（tz）f（tz）dt/t.