R. de la Llave
Bootstrap of regularity for integrable solutions of cohomology equations
(41K, LaTeX2e)

ABSTRACT.  We present an elementary argument to bootstrap the regularity of
integrable solutions of cohomology equations.
if $f:M \to M$ is  a smooth Anosov (partially hyperbolic with uniform
accessibility) we show that if $\varphi \in L^p$, $\eta \in C^\beta$,
$\beta > 0$
and 
\[
\varphi =\eta \varphi \circ f,
\]
$p$ 
high enough,  then $\varphi \in \alpha'$, 
where $\beta'$ depends on the hyperbolicity properties 
of $f$. ($\beta' = \beta$ if $f$ is Anosov.)