论文标题
Riesz-Kolmogorov类型的紧凑标准在功能空间中具有应用
Riesz-Kolmogorov type compactness criteria in function spaces with applications
论文作者
论文摘要
我们介绍了经典的Riesz-Kolmogorov定理的紧凑性，这些形式适用于各种环境。特别是，我们的定理适用于Lebesgue Space $ l^2 $，Paley-Wiener空间，加权Bargmann-Fock空间以及一系列加权BESOV-SOBOLOLEV空间的规模分类，其中包括一般性伯格曼空间的加权伯格曼空间，以及艰难的空间和迪利奇（Dirich）空间。我们应用紧凑的标准来表征伯格曼空间上紧凑的托管操作员，推断出汉克尔算子在耐力空间上的紧凑性，并获得一般的伞定理。
We present forms of the classical Riesz-Kolmogorov theorem for compactness that are applicable in a wide variety of settings. In particular, our theorems apply to classify the precompact subsets of the Lebesgue space $L^2$, Paley-Wiener spaces, weighted Bargmann-Fock spaces, and a scale of weighted Besov-Sobolev spaces of holomorphic functions that includes weighted Bergman spaces of general domains as well as the Hardy space and the Dirichlet space. We apply the compactness criteria to characterize the compact Toeplitz operators on the Bergman space, deduce the compactness of Hankel operators on the Hardy space, and obtain general umbrella theorems.
