有限和infinite dimensional状态空间上一类（伪）微分算子的Schauder定理
Schauder theorems for a class of (pseudo-)differential operators on finite and infinite dimensional state spaces
摘要：
我们证明了在Hölder和Zygmund空间中由一大类微分算子和伪微分算子L驱动的线性平稳和发展方程的极大正则性结果，包括有限维和无限维。这些假设是根据L生成的半群给出的。我们涵盖了有限维中具有分数扩散的分数Laplacian算子和Ornstein-Uhlenbeck算子的情形，以及无穷维中的几种局部和非局部Ornstein-Uhlenbeck算子，以及Gross Laplacian算子及其负幂.
英文摘要：
We prove maximal regularity results in Hölder and Zygmund spaces for linear stationary and evolution equations driven by a large 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 negative powers, in infinite dimension.
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