  Let G be a locally compact abelian group and let \mu be a complex valued
regular Borel measure on G. In this paper we consider a generalisation of a
class of Banach lattices introduced in [6]. We use Laplace transform methods to
show that the norm of a convolution operator with symbol \mu on such a space is
bounded below by the L_\infty norm of the Fourier-Stieltjes transform of \mu.
We also show that for any Banach lattice of locally integrable functions on G
with a shift-invariant norm, the norm of a convolution operator with symbol \mu
is bounded above by the total variation of \mu.
