  We develop operator renewal theory for flows and apply this to infinite
ergodic theory. In particular we obtain results on mixing for a large class of
infinite measure semiflows.
  Examples of systems covered by our results include suspensions over parabolic
rational maps of the complex plane, and nonuniformly expanding semiflows with
indifferent periodic orbits. In some cases, we obtain higher order asymptotics
and rates of mixing.
