Singular convolution integrals with operator-valued kernel

We study operators f -> Kf of the form (Kf)(t) = integral(Rn)k(t-s)f(s) ds, where f is a vector-valued function and k an operator-valued singular kernel. Sufficient conditions for boundedness on L-p supercript stop-spaces of UMD-valued functions are given in terms of a Hormander-type condition involving R-boundedness. The results cover large classes of kernels and also provide new proofs of recent operator-valued Fourier multiplier theorems. Moreover, they give new information about families of singular integral operators.