  We study a large class of suspension semiflows which contains the Lorenz
semiflows. This is a class with low regularity (merely C^{1+\alpha}) and where
the return map is discontinuous and the return time is unbounded. We establish
the functional analytic framework which is typically employed to study rates of
mixing. The Laplace transform of the correlation function is shown to admit a
meromorphic extension to a strip about he imaginary axis. As part of this
argument we give a new result concerning the quasi-compactness of weighted
transfer operators for piecewise C^{1+\alpha} expanding interval maps.
