We provide here global Schauder-type estimates for a chain of integro-partial differential equations (IPDE) driven by a degenerate stable Ornstein-Uhlenbeck operator possibly perturbed by a deterministic drift, when the coefficients lie in some suitable anisotropic Hölder spaces. Our approach mainly relies on a perturbative method based on forward parametrix expansions and, due to the low regularizing properties on the degenerate variables and to some integrability constraints linked to the stability index, it also exploits duality results between appropriate Besov Spaces. In particular, our method also applies in some super-critical cases. Thanks to these estimates, we show in addition the well-posedness of the considered IPDE in a suitable functional space.

当系数位于某个合适的各向异性Hölder空间中时，我们在这里提供由退化稳定Ornstein-Uhlenbeck算子驱动的一连串积分-偏微分方程（IPDE）的全局Schauder型估计。我们的方法主要依赖于基于正向参数扩展的摄动方法，并且由于退化变量的正则化特性低以及与稳定性指数相关的一些可积性约束，它还利用了适当的Besov空间之间的对偶结果。特别是，我们的方法还适用于某些超临界情况。由于这些估计，我们还显示了在适当的功能空间中考虑的IPDE的适定性。