Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups

Guorong Hu

Czechoslovak Mathematical Journal (2019)

  • Volume: 69, Issue: 1, page 131-159
  • ISSN: 0011-4642

Abstract

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We give a characterization of the Hölder-Zygmund spaces 𝒞 σ ( 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.

How to cite

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Hu, Guorong. "Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups." Czechoslovak Mathematical Journal 69.1 (2019): 131-159. <http://eudml.org/doc/294365>.

@article{Hu2019,
abstract = {We give a characterization of the Hölder-Zygmund spaces $\mathcal \{C\}^\{\sigma \}(G)$ ($0< \sigma <\infty $) 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.},
author = {Hu, Guorong},
journal = {Czechoslovak Mathematical Journal},
keywords = {stratified Lie group; Hölder-Zygmund space; Littlewood-Paley decomposition},
language = {eng},
number = {1},
pages = {131-159},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups},
url = {http://eudml.org/doc/294365},
volume = {69},
year = {2019},
}

TY - JOUR
AU - Hu, Guorong
TI - Littlewood-Paley characterization of Hölder-Zygmund spaces on stratified Lie groups
JO - Czechoslovak Mathematical Journal
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 131
EP - 159
AB - We give a characterization of the Hölder-Zygmund spaces $\mathcal {C}^{\sigma }(G)$ ($0< \sigma <\infty $) 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.
LA - eng
KW - stratified Lie group; Hölder-Zygmund space; Littlewood-Paley decomposition
UR - http://eudml.org/doc/294365
ER -

References

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