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Czechoslovak Mathematical Journal

, Volume 69, Issue 1, pp 131–159 | Cite as

Littlewood-Paley Characterization of Hölder-Zygmund Spaces on Stratified Lie Groups

  • Guorong HuEmail author
Article
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Abstract

We give a characterization of the Hölder-Zygmund spaces Cσ(G) (0 < σ < ∞) on a stratified Lie group G in terms of Littlewood-Paley type decompositions, in analogy to the well-known characterization of the Euclidean case. Such decompositions are defined via the spectral measure of a sub-Laplacian on G, in place of the Fourier transform in the classical setting. Our approach mainly relies on almost orthogonality estimates and can be used to study other function spaces such as Besov and Triebel-Lizorkin spaces on stratified Lie groups.

Keywords

stratified Lie group Hölder-Zygmund space Littlewood-Paley decomposition 

MSC 2010

43A80 42B25 42B35 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.Department of MathematicsJiangxi Normal UniversityNanchang, JiangxiP.R. China

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