Atomic and Molecular Decomposition of Homogeneous Spaces of Distributions Associated to Non-negative Self-Adjoint Operators

被引：0
作者：
A. G. Georgiadis
G. Kerkyacharian
G. Kyriazis
P. Petrushev
机构：
[1] University of Cyprus,Department of Mathematics and Statistics
[2] Laboratoire de Probabilités et Modèles Aléatoires,Department of Mathematics
[3] CNRS-UMR 7599,undefined
[4] Crest,undefined
[5] University of South Carolina,undefined
来源：
Journal of Fourier Analysis and Applications | 2019年 / 25卷
关键词：
Algebra; Almost diagonal operators; Atomic decomposition; Besov spaces; Frames; Heat kernel; Homogeneous spaces; Molecular decomposition; Spectral multipliers; Triebel–Lizorkin spaces; Primary 58J35; 46E35; 43A85; Secondary 42B25; 42B15; 42C15; 42C40;
D O I：
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学科分类号：
摘要：
We deal with homogeneous Besov and Triebel–Lizorkin spaces in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel–Lizorkin spaces. Spectral multipliers for these spaces are established as well.
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页码：3259 / 3309
页数：50
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