Pluricapacity and approximation numbers of composition operators

Abstract For suitable bounded hyperconvex sets Ω in C N , in particular the ball or the polydisk, we give estimates for the approximation numbers of composition operators C φ : H 2 ( Ω ) → H 2 ( Ω ) when φ ( Ω ) is relatively compact in Ω, involving the Monge–Ampere capacity of φ ( Ω ) .