  We show that the Hamiltonian action satisfies the Palais-Smale condition over
a "mixed regularity" space of loops in cotangent bundles, namely the space of
loops with regularity $H^s$, $s\in (\frac 12, 1)$, in the base and $H^{1-s}$ in
the fiber direction. As an application, we give a simplified proof of a theorem
of Hofer-Viterbo on the existence of closed characteristic leaves for certain
contact type hypersufaces in cotangent bundles.
