Product Besov and Triebel–Lizorkin Spaces with Application to Nonlinear Approximation
Product Besov and Triebel–Lizorkin Spaces with Application to Nonlinear Approximation
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DOI：
10.1007/s00365-019-09490-1
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发表时间：
2019-12
影响因子：
2.7
通讯作者：
A. G. Georgiadis;G. Kyriazis;P. Petrushev
中科院分区：
文献类型：
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作者：
A. G. Georgiadis;G. Kyriazis;P. Petrushev
齐次积 Besov 和 Triebel-Lizorkin 空间的 Littlewood-Paley 理论是本着 Frazier 和 Jawerth 变换的精神发展起来的。这包括积 Besov 和 Triebel-Lizorkin 空间的框架表征以及这些空间上几乎对角算子的开发。几乎对角算子用于获得积 Besov 和 Triebel-Lizorkin 空间的积小波分解。该理论的主要应用是哈代空间中乘积小波的非线性项近似。 Sharp Jackson 和 Bernstein 的估计是根据乘积贝索夫空间获得的。
The Littlewood–Paley theory of homogeneous product Besov and Triebel–Lizorkin spaces is developed in the spirit of the-transform of Frazier and Jawerth. This includes the frame characterization of the product Besov and Triebel–Lizorkin spaces and the development of almost diagonal operators on these spaces. The almost diagonal operators are used to obtain product wavelet decomposition of the product Besov and Triebel–Lizorkin spaces. The main application of this theory is to nonlinearm-term approximation from product wavelets inand Hardy spaces. Sharp Jackson and Bernstein estimates are obtained in terms of product Besov spaces.