On the cohomological equation for interval exchange maps

We exhibit an explicit full measure class of minimal interval exchange maps T for which the cohomological equation Ψ−Ψ∘T=Φ has a bounded solution Ψ provided that the datum Φ belongs to a finite codimension subspace of the space of functions having on each interval a derivative of bounded variation. The class of interval exchange maps is characterized in terms of a diophantine condition of “Roth type” imposed to an acceleration of the Rauzy–Veech–Zorich continued fraction expansion associated to T.