02-378 R. de la Llave
Bootstrap of regularity for integrable solutions of cohomology equations (41K, LaTeX2e) 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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