中文摘要：

本文研究多复变数单位球上的Carleson测度＋利用Bloch函数对有界及消没对数Carleson测度进行刻画，得到了在Bloch空间上类似于Hardy空间和Bergman空间上的Carleson定理．并推广的Cesáro算子在Bloch空间上有界和紧的等价条件．

英文摘要：

In this paper, we investigate the logarithmic Carleson measures on the unit ball, and characterize the hounded and vanishing logarithmic Carleson measures in terms of Bloeh functions. We obtain the analogous result on Bloch space to the Carleson theorem on the Hardy spaces and Bergman spaces. As an application, we give the equivalent condition of boundedness and compactness of the extended Cesáro operator on the Bloch space.