How to measure smoothness of distributions on Riemannian symmetric manifolds and Lie group?
type: Item
instance of: scholarly article
title: How to measure smoothness of distributions on Riemannian symmetric manifolds and Lie group?
zbMATH Open document ID: 0685.46020
DOI: 10.4171/ZAA/321
author: Hans Triebel
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 1988-01-01T00:00:00Z
review text: The author considers some types of Riemannian manifolds, hyperbolic manifolds and Lie groups, and function spaces connected with them. In particular, he introduces two scales of function spaces on them which cover such classical function spaces as the Hölder-Zygmund, Besov, Sobolev, and Hardy spaces. The smoothness of distributions is measured via introduced means over the above mentioned structures. The considerations are restricted to the case of globally symmetric manifolds to allow the use of Fourier analytical tools, spectral means and convolutions.
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 4122614
zbMATH Keywords: Riemannian manifolds
zbMATH Keywords: hyperbolic manifolds
zbMATH Keywords: Lie groups
zbMATH Keywords: scales of function spaces
zbMATH Keywords: Hölder-Zygmund
zbMATH Keywords: Besov
zbMATH Keywords: Sobolev
zbMATH Keywords: Hardy spaces
zbMATH Keywords: smoothness of distributions
zbMATH Keywords: globally symmetric manifolds
zbMATH Keywords: Fourier analytical tools
zbMATH Keywords: spectral means
zbMATH Keywords: convolutions
reviewed by: Pawel Kruszynski
MaRDI profile type: Publication
Wikidata QID: Q115211705
full work available at URL: https://doi.org/10.4171/zaa/321
OpenAlex ID: W2562566589
description: scientific article; zbMATH DE number 4122614