Essential norms of the extended Cesàro operators on Bergman spaces with exponential weight in the unit ball

Zhi-Jie Jiang, Zuo-An Li, Xiao-Feng Wang

Let B n = {z ∈ C n : |z| < 1} be the unit ball of the complex n-plane C n , a holomorphic function in B n and A 2 α,β (B n) the space of holomorphic functions that are L 2 with respect to a rapidly decreasing weight of form ω α,β (z) = (1 − |z|) α e − β 1−|z| on B n , where α ∈ R and β > 0. In this paper, we compute the essential norm of the extended Cesàro operator T on A 2 α,β (B n). As a direct application, we obtain the essential norm for the one-variable case.