Besov and Hardy spaces associated with the Schrödinger operator on the Heisenberg group
type: Item
instance of: scholarly article
title: Besov and Hardy spaces associated with the Schrödinger operator on the Heisenberg group
zbMATH Open document ID: 1321.47102
author: Ruming Gong
author: Liang Song
author: Ji Li
published in: The Journal of Geometric Analysis
publication date: 2014-11-18T00:00:00Z
review text: Consider the Schrödinger operator \(L=-\Delta_{{\mathbb{H}}^n}+V\) on the Heisenberg group \( \mathbb{H}^n\), where \(\Delta_{\mathbb{H}^n}\) is the sub-Laplacian on \(\mathbb{H}^n\) and \(V\) is in the reverse Hölder class \(B_q\) with \(q \geq n+1\). In this paper, the Besov space \(\dot{B}_{1,1}^{0, L}\) and the Hardy space \(H_{L}^{1}\) associated with \(L\) are defined by the heat semigroup and the Littlewood-Paley area function, respectively, and then characterized in terms of atomic and molecular decomposition. Consequently, it is shown that \(\dot{B}_{1,1}^{0, L}\) is a subspace of \(H_{L}^{1}\).
reviewed by: Miyeon Kwon
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 43A15
zbMATH DE Number: 6370382
zbMATH Keywords: Schrödinger operator
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Besov space
zbMATH Keywords: Hardy space
zbMATH Keywords: Littlewood-Paley square function
zbMATH Keywords: molecule
zbMATH Keywords: atom
MaRDI profile type: Publication
full work available at URL: s12220-012-9331-3
OpenAlex ID: W2076089599
cites work: Hardy spaces of differential forms on Riemannian manifolds
cites work: Q4855888
cites work: Q4890733
cites work: Calderón reproducing formulas and new Besov spaces associated with operators
cites work: A T(b) theorem with remarks on analytic capacity and the Cauchy integral
cites work: Q2548398
cites work: Besov spaces with non-doubling measures
cites work: Duality of Hardy and BMO spaces associated with operators with heat kernel bounds
cites work: Hardy space \(H^1\) associated to Schrödinger operator with potential satisfying reverse Hölder inequality
cites work: The uncertainty principle
cites work: Q3344703
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Q3721264
cites work: Hardy spaces associated to non-negative self-adjoint operators satisfying Davies-Gaffney estimates
cites work: Hardy and BMO spaces associated to divergence form elliptic operators
cites work: Q3780156
cites work: \(L^p\) estimates of Schrödinger operators on nilpotent groups
cites work: \(BMO_L(\mathbb H^n)\) spaces and Carleson measures for Schrödinger operators
cites work: Q4339422
cites work: Q4674789
cites work: Q3548322
cites work: \(L^ p\) estimates for Schrödinger operators with certain potentials
cites work: Brownian motion characterization of some Besov--Lipschitz spaces on domains
cites work: Q3142876
DOI: 10.1007/S12220-012-9331-3
description: scientific article; zbMATH DE number 6370382