Pluricapacity and approximation numbers of composition operators

Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza, Hervé Queélec

Published 2018-09-24Version 1

For suitable bounded hyperconvex sets $\Omega$ in $\mathbb{C}^N$, in particular the ball or the polydisk, we give estimates for the approximation numbers of composition operators $C_\phi \colon H^2 (\Omega) \to H^2 (\Omega)$ when $\phi (\Omega)$ is relatively compact in $\Omega$, involving the Monge-Amp\`ere capacity of $\phi (\Omega)$.