Decay of Correlations via induced Weak Gibbs Markov maps for non-H\"{o}lder observables

We extend the results of [Ullah, A., Vilarinho, H,.: Statistical properties of dynamical systems via induced weak Gibbs Markov maps. arXiv:2311.17531 (2023)] by considering larger classes of observables. More precisely, we obtain estimates on the decay of correlations, Central Limit Theorem and Large Deviations for dynamical systems having an induced weak Gibbs Markov map, for larger classes of observables with weaker regularity than H\"{o}lder.