1 Elementary Results.- 2 An Approximation Theorem for CV2(G).- 3 The Figa-Talamanca Herz Algebra.- 4 The Dual of Ap(G).- 5 CVp(G) as a Module on Ap(G).- 6 The Support of a Convolution Operator.- 7 Convolution Operators Supported by Subgroups.- 8 CVp(G) as a Subspace of CV2(G).