Pluricapacity and approximation numbers of composition operators

Abstract

For suitable bounded hyperconvex sets $\hat{I}\text{c◯}$ in ${\mathbb{C}}^N$, in particular the ball or the polydisk, we give estimates for the approximation numbers of composition operators $C_{\ddot{I}}•:H^2(\hat{I}\text{c◯})\to H^2(\hat{I}\text{c◯})$ when $\ddot{I}•(\hat{I}\text{c◯})$ is relatively compact in $\hat{I}\text{c◯}$, involving the Monge-Ampère capacity of $\ddot{I}•(\hat{I}\text{c◯})$.