Entropy Numbers of Finite Dimensional Mixed-Norm Balls and Function Space Embeddings with Small Mixed Smoothness
Entropy Numbers of Finite Dimensional Mixed-Norm Balls and Function Space Embeddings with Small Mixed Smoothness
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DOI：
10.1007/s00365-020-09510-5
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发表时间：
2019-04
影响因子：
2.7
通讯作者：
Sebastian Mayer;T. Ullrich
中科院分区：
文献类型：
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作者：
Sebastian Mayer;T. Ullrich
我们研究了熵值的嵌入，并证明了熵值的匹配界。基于这一发现，我们建立了Besov和triiebel - lizorkin小支配混合光滑空间嵌入的熵数的最优无维渐近率，从而给出了Dũng、Temlyakov和Ullrich最近的专著中提到的一个开放问题的完整答案。这两个结果都依赖于Edmunds和Netrusov最近发现的一种新的覆盖结构。
We study the embeddingand prove matching bounds for the entropy numbersprovided thatand. Based on this finding, we establish optimal dimension-free asymptotic rates for the entropy numbers of embeddings of Besov and Triebel–Lizorkin spaces ofsmalldominating mixed smoothness, which gives a complete answer to an open problem mentioned in the recent monograph by Dũng, Temlyakov, and Ullrich. Both results rely on a novel covering construction recently found by Edmunds and Netrusov.