Product Besov and Triebel-Lizorkin Spaces with Application to Nonlinear Approximation

被引：7
|
作者：
Georgiadis, Athanasios G. [1 ]
Kyriazis, George [1 ]
Petrushev, Pencho [2 ]
机构：
[1] Univ Cyprus, Dept Math & Stat, Nicosia, Cyprus
[2] Univ South Carolina, Dept Math, Columbia, SC 29208 USA
来源：
CONSTRUCTIVE APPROXIMATION | 2021年 / 53卷 / 01期
关键词：
Product spaces; Besov spaces; Triebel-Lizorkin spaces; phi-Transform; Wavelets; Nonlinear approximation; Jackson estimate; Bernstein estimate; HP-THEORY; DECOMPOSITION; BASES;
D O I：
10.1007/s00365-019-09490-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Littlewood-Paley theory of homogeneous product Besov and Triebel-Lizorkin spaces is developed in the spirit of the phi-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 and Hardy spaces. Sharp Jackson and Bernstein estimates are obtained in terms of product Besov spaces.
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页码：39 / 83
页数：45
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