We consider a class of endomorphisms which contains a set of piecewise partially hyperbolic skew-products with a non-uniformly expanding base map. The aimed transformation preserves a foliation which is almost everywhere uniformly contracted with possible discontinuity sets, which are parallel to the contracting direction. We prove that the associated transfer operator, acting on suitable anisotropic normed spaces, has a spectral gap (on which we have quantitative estimation) and the disintegration of the unique invariant physical measure, along the stable leaves, is $\zeta$-Holder. We use this fact to obtain exponential decay of correlations on the set of $\zeta$-Holder functions.

中文翻译：

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一类分段部分双曲线映射的 Hölder 正则性和相关性指数衰减

我们考虑一类自同态，它包含一组具有非均匀扩展底图的分段部分双曲斜积。目标变换保留了几乎处处均匀收缩的叶理，可能的不连续集与收缩方向平行。我们证明了相关的转移算子，作用于合适的各向异性赋范空间，具有谱间隙（我们对其进行定量估计），并且沿着稳定叶的独特不变物理测度的分解是 $\zeta$-Holder。我们使用这个事实来获得 $\zeta$-Holder 函数集上相关性的指数衰减。