Lipschitz conditions in Damek-Ricci spaces
type: Item
instance of: scholarly article
title: Lipschitz conditions in Damek-Ricci spaces
zbMATH Open document ID: 1483.43007
author: S. El Ouadih
author: Radouan Daher
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2021-09-03T00:00:00Z
review text: The paper gives a complete characterization of the (Dini-) Lipschitz conditions for $L^2$ space on Damek-Ricci spaces by estimating the norm of the Fourier-Helgason transform. A necessary characterization of the (Dini-) Lipschitz conditions for the $L^p$ space when $1< p< 2$ is nicely presented. Furthermore, the norm of the Fourier-Helgason transform is also estimated for functions in the (Dini-) Lipschitz class. The results greatly improve the ones obtained by \textit{E. C. Titchmarsh} [Introduction to the theory of Fourier integrals. Oxford: Clarendon Press (1937; Zbl 0017.40404)].
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 42B10
zbMATH DE Number: 7390651
zbMATH Keywords: Fourier-Helgason transform
zbMATH Keywords: Damek-Ricci spaces
reviewed by: Jinsong Wu
MaRDI profile type: Publication
full work available at URL: crmath.211
OpenAlex ID: W3194945764
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DOI: 10.5802/CRMATH.211
description: scientific article; zbMATH DE number 7390651