Function spaces with dominating mixed smoothness
Function spaces with dominating mixed smoothness
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DOI：
10.4064/dm436-0-1
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发表时间：
2006
影响因子：
1.8
通讯作者：
J. Vybíral
中科院分区：
文献类型：
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作者：
J. Vybíral
我们研究了Besov和triiebelizorkin空间中一些众所周知的技术，并将它们推广到具有主导混合光滑性的空间。我们用triiebel的思想证明了三个重要的分解定理。我们处理所谓的原子分解，亚原子分解和小波分解。所有这些定理都有很多共同之处。简单地说，他们说一个函数属于某个函数空间当且仅当，它可以被分解成系数和相应构件的乘积的和，其中系数属于一个适当的序列空间。这些分解定理在函数空间和序列空间之间建立了非常有用的联系。我们将它们用于研究两个占主导地位的混合光滑函数空间之间紧嵌入的熵数衰减问题，并在序列空间水平上将其简化为同一个问题。考虑的尺度涵盖了许多重要的特定空间（Sobolev, Zygmund, Besov），我们得到了Belinsky， Dinh Dung和Temlyakov各自断言的概括。
We study several techniques whichare well known in the case of Besov and TriebelLizorkin spaces and extend them to spaces with dominating mixed smoothness. We use the ideas of Triebel to prove three important decomposition theorems. We deal withsocalled atomic, subatomic and wavelet decompositions. All these theorems have much in common. fRoughly speaking, they say that a function belongs to some function space if, and only if, it can be decomposed into the sum of products of coefficients and corresponding building blocks, where the coefficients belong to an appropriate sequence space. These decomposition theorems estabilisha veryusefulconnection between function and sequence spaces. We use them in the study of the decay of entropy numbers of compact embeddings between two function spaces of dominating mixed smoothness reducingthis problem to the same question on the sequence space level. The considered scales cover many important specific spaces (Sobolev, Zygmund, Besov) and we get generalisations of respective assertions of Belinsky, Dinh Dung and Temlyakov.