The Essential Norm of Operators on $A^p_\alpha(\mathbb{B}_n)$
  In this paper we characterize the compact operators on $A^p_\alpha(\mathbb{B}_n)$ when $1<p<\infty$ and $\alpha>-1$. The main result shows that an operator on $A^p_\alpha(\mathbb{B}_n)$ is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball. 
Mishko Mitkovski, Daniel Su\'arez, Brett D. Wick
math.CA math.CV