The Littlewood–Paley theory of homogeneous product Besov and Triebel–Lizorkin spaces is developed in the spirit of the $$\varphi $$ φ -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 nonlinear m -term approximation from product wavelets in $$L^p$$ L p and Hardy spaces. Sharp Jackson and Bernstein estimates are obtained in terms of product Besov spaces.

中文翻译：

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乘积 Besov 和 Triebel-Lizorkin 空间在非线性逼近中的应用

齐次积 Besov 和 Triebel-Lizorkin 空间的 Littlewood-Paley 理论是在 Frazier 和 Jawerth 的 $$\varphi $$ φ 变换的精神下发展起来的。这包括积 Besov 和 Triebel-Lizorkin 空间的框架特征以及在这些空间上开发几乎对角线算子。近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从 $$L^p$$L p 和 Hardy 空间中的乘积小波的非线性 m 项逼近。Sharp Jackson 和 Bernstein 估计是根据乘积 Besov 空间获得的。