Riesz–Kolmogorov Type Compactness Criteria in Function Spaces with Applications
Riesz–Kolmogorov Type Compactness Criteria in Function Spaces with Applications
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DOI：
10.1007/s11785-023-01346-8
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发表时间：
2022-04
影响因子：
0.8
通讯作者：
Mishko Mitkovski;Cody B. Stockdale;Nathan A. Wagner;B. Wick
中科院分区：
文献类型：
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作者：
Mishko Mitkovski;Cody B. Stockdale;Nathan A. Wagner;B. Wick
我们提出的形式的经典Riesz-Kolmogorov定理的紧凑性，适用于各种各样的设置。特别地，我们的定理适用于分类的勒贝格空间，Paley-Wiener空间，加权Bargmann-Fock空间，和一个规模的加权Besov-Sobolev空间的全纯函数，包括加权Bergman空间的一般域以及哈代空间和Dirichlet空间的预紧子集。利用紧性准则刻画了Bergman空间上的紧Toeplitz算子，导出了Hankel算子在哈代空间上的紧性，得到了一般的伞形定理.
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, 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.