  For Axiom A flows on basic sets satisfying certain additional conditions we
prove strong spectral estimates for Ruelle transfer operators similar to these
of Dolgopyat (1998) for geodesic flows on compact surfaces (for general
potentials)and transitive Anosov flows on compact manifolds with C^1 jointly
non-integrable horocycle foliations (for the Sinai-Bowen-Ruelle potential).
Here we deal with general potentials. As is now well known, such results have
deep implications in some related areas, e.g. in studying analytic properties
of Ruelle zeta functions and partial differential operators, closed orbit
counting functions, decay of correlations for H\"older continuous potentials.
