Norms of Iterates of Volterra Operators on L^2

It has recently been established that if V is the classical Volterra (indefinite integration) operator acting on the Hilbert space L2([0, 1]), then the operator and Hilbert-Schmidt norms of V n are both asymptotically 1/(2n!). We extend this in two ways: firstly, we give a generalisation which applies to Volterra convolution operators with kernels satisfying a mild smoothness condition, and secondly we show that in the constant-kernel case the same asymptotic behaviour is shared by the trace norm, and hence by a wide class of operator norms.