We prove maximal regularity results in Hölder and Zygmund spaces for linear stationary and evolution equations driven by a class of differential and pseudo-differential operators $L$, both in finite and in infinite dimension. The assumptions are given in terms of the semigroup generated by $L$. We cover the cases of fractional Laplacians and Ornstein–Uhlenbeck operators with fractional diffusion in finite dimension, and several types of local and nonlocal Ornstein–Uhlenbeck operators, as well as the Gross Laplacian and its fractional powers, in infinite dimension.

中文翻译：

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有限维和无限维状态空间上一类（伪）微分算子的 Schauder 定理

我们证明了由一类微分和伪微分算子驱动的线性平稳方程和演化方程在 Hölder 和 Zygmund 空间中的最大正则性结果 $升$，在有限维和无限维上。假设是根据由以下生成的半群给出的$升$. 我们涵盖了分数拉普拉斯算子和 Ornstein-Uhlenbeck 算子在有限维中具有分数扩散的情况，以及几种类型的局部和非局部 Ornstein-Uhlenbeck 算子，以及无限维中的 Gross Laplacian 及其分数幂。