\(H^ p\)-multipliers on stratified groups
type: Item
instance of: scholarly article
title: \(H^ p\)-multipliers on stratified groups
zbMATH Open document ID: 0638.43007
DOI: 10.1007/BF01774295
author: Giancarlo Mauceri
author: Leonede De-Michele
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1987-01-01T00:00:00Z
review text: The authors give a criterion for boundedness on the Hardy spaces \(H^ p\) for functions M(\({\mathcal L})\) of the sublaplacian \({\mathcal L}\) on a stratified Lie group, when M is bounded, and M and its dilates M(R\(\lambda)\), \(R>0\), are locally in the Lipschitz-Besov space \(\Lambda\) (s;\(\tau\),\(\infty)\) uniformly with respect to R. The criterion requires that \(r>0\) (not necessarily an integer), \(s>r+(Q/2)+1\) and \(Q(Q+r)<p<\infty\), where Q is the homogeneous dimension of the group. The proof is based on the atomic and molecular characterization of Hardy spaces.
reviewed by: Takahiko Nakazi
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 44A30
Mathematics Subject Classification ID: 44A10
zbMATH DE Number: 4040531
zbMATH Keywords: Besov condition
zbMATH Keywords: multiplier
zbMATH Keywords: Hardy spaces
zbMATH Keywords: sublaplacian
zbMATH Keywords: stratified Lie group
zbMATH Keywords: Lipschitz-Besov space
MaRDI profile type: Publication
cites work: Embedding and multiplier theorems for 𝐻^{𝑃}(𝑅ⁿ)
cites work: Characterization of Fourier Transforms of Hardy Spaces
cites work: Q3925395
cites work: Parabolic maximal functions associated with a distribution. II
cites work: Extensions of Hardy spaces and their use in analysis
cites work: \(L^p\) multipliers on the Heisenberg group
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Croissance polynomiale et périodes des fonctions harmoniques
cites work: Subalgebra of $L_1(G)$ associated with Laplacian on a Lie group
cites work: Commutative subalgebra of 𝐿¹(𝐺) associated with a subelliptic operator on a Lie group 𝐺
cites work: Almost Everywhere Summability on Nilmanifolds
cites work: Zonal multipliers on the Heisenberg group
cites work: Q3808333
cites work: Q3871351
cites work: Q3925396
full work available at URL: https://doi.org/10.1007/bf01774295
OpenAlex ID: W2068857554
description: scientific article; zbMATH DE number 4040531