We show that if V α (α > 0) is the Riemann-Liouville fractional integration operator and T is an invertible operator on L 2(0, 1) which commutes with V , then TV α is not supercyclic on L 2(0, 1); in particular, many Volterra convolution operators are not supercyclic. The technique is based on an argument used by Gallardo-Gutierrez and Montes-Rodriguez to show that V is not supercyclic.