Spaces of Besov-Sobolev type and a problem on nonlinear approximation
Spaces of Besov-Sobolev type and a problem on nonlinear approximation
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DOI：
10.1016/j.jfa.2022.109775
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发表时间：
2021-12
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影响因子：
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通讯作者：
'Oscar Dom'inguez;A. Seeger;B. Street;Jean Van Schaftingen;Po-Lam Yung
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作者：
'Oscar Dom'inguez;A. Seeger;B. Street;Jean Van Schaftingen;Po-Lam Yung
我们研究了由Brezis、Van Schaftingen和Yung在Sobolev空间W˙1，p的研究中引入的拟范数的分数变体。由此产生的空间被识别为Sobolev- slobodecki空间的一类特殊实插值空间。通过作用于可测函数的差分算子，建立了傅里叶解析定义与定义之间的等价性。我们证明了关于嵌入和非嵌入的各种新结果，并给出了谐波和热量扩展的应用。对于合适的小波基，我们通过函数的光滑性条件，得到了小波基上最佳n项逼近的逼近空间的表征；这扩展了DeVore， Jawerth和Popov的经典结果。
We study fractional variants of the quasi-norms introduced by Brezis, Van Schaftingen, and Yung in the study of the Sobolev space W˙ 1, p. The resulting spaces are identified as a special class of real interpolation spaces of Sobolev-Slobodeckiĭ spaces. We establish the equivalence between Fourier analytic definitions and definitions via difference operators acting on measurable functions. We prove various new results on embeddings and non-embeddings, and give applications to harmonic and caloric extensions. For suitable wavelet bases we obtain a characterization of the approximation spaces for best n-term approximation from a wavelet basis via smoothness conditions on the function; this extends a classical result by DeVore, Jawerth and Popov.