Abstract
Let Bn = {z ? Cn : |z| < 1} be the unit ball of the complex n-plane Cn, 1 a holomorphic function in Bn and A2 ?,? (Bn) the space of holomorphic functions that are L2 with respect to a rapidly decreasing weight of form ??,?(z) = (1 ? |z|)?e? ? 1?|z| on Bn, where ? ? R and ? > 0. In this paper, we compute the essential norm of the extended Ces?ro operator T1 on A2 ?,? (Bn). As a direct application, we obtain the essential norm for the one-variable case.
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