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Abstract in UndeterminedWe consider the regularity of measurable solutions $ \chi$ to the cohomological equation$\displaystyle \phi = \chi \circ T -\chi, $where $ (T,X,\mu)$ is a dynamical system and $ \phi \colon X\rightarrow \mathbb{R}$ is a $ C^k$ smooth real-valued cocycle in the setting in which $ T \colon X\rightarrow X$ is a piecewise $ C^k$ Gibbs-Markov map, an affine $ \beta$-transformati
