Compact composition operators on the Smirnov class

We show that a composition operator on the Smirnov class N+ is compact if a nd only if it is compact on some (equivalently: every) Hardy space H-p for 0 < p < infinity. Along the way we show that for composition operators on N + both the formally weaker notion of boundedness, and a formally stronger n otion we call metric compactness, are equivalent to compactness.