- 02-378 R. de la Llave
- Bootstrap of regularity for integrable solutions of cohomology equations
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Sep 12, 02
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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.)
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