Commutators associated with Schrödinger operators on the nilpotent Lie group

Assume that G is a nilpotent Lie group. Denote by [Formula: see text] the Schrödinger operator on G, where Δ is the sub-Laplacian, the nonnegative potential W belongs to the reverse Hölder class [Formula: see text] for some [Formula: see text] and D is the dimension at infinity of G. Let [Formula: s...

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Detalles Bibliográficos
Autores principales: Ni, Tianzhen, Liu, Yu
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5736795/
https://www.ncbi.nlm.nih.gov/pubmed/29290667
http://dx.doi.org/10.1186/s13660-017-1584-8
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author Ni, Tianzhen
Liu, Yu
author_facet Ni, Tianzhen
Liu, Yu
author_sort Ni, Tianzhen
collection PubMed
description Assume that G is a nilpotent Lie group. Denote by [Formula: see text] the Schrödinger operator on G, where Δ is the sub-Laplacian, the nonnegative potential W belongs to the reverse Hölder class [Formula: see text] for some [Formula: see text] and D is the dimension at infinity of G. Let [Formula: see text] be the Riesz transform associated with L. In this paper we obtain some estimates for the commutator [Formula: see text] for [Formula: see text] , where [Formula: see text] is a function space which is larger than the classical Lipschitz space.
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spelling pubmed-57367952017-12-29 Commutators associated with Schrödinger operators on the nilpotent Lie group Ni, Tianzhen Liu, Yu J Inequal Appl Research Assume that G is a nilpotent Lie group. Denote by [Formula: see text] the Schrödinger operator on G, where Δ is the sub-Laplacian, the nonnegative potential W belongs to the reverse Hölder class [Formula: see text] for some [Formula: see text] and D is the dimension at infinity of G. Let [Formula: see text] be the Riesz transform associated with L. In this paper we obtain some estimates for the commutator [Formula: see text] for [Formula: see text] , where [Formula: see text] is a function space which is larger than the classical Lipschitz space. Springer International Publishing 2017-12-19 2017 /pmc/articles/PMC5736795/ /pubmed/29290667 http://dx.doi.org/10.1186/s13660-017-1584-8 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Ni, Tianzhen
Liu, Yu
Commutators associated with Schrödinger operators on the nilpotent Lie group
title Commutators associated with Schrödinger operators on the nilpotent Lie group
title_full Commutators associated with Schrödinger operators on the nilpotent Lie group
title_fullStr Commutators associated with Schrödinger operators on the nilpotent Lie group
title_full_unstemmed Commutators associated with Schrödinger operators on the nilpotent Lie group
title_short Commutators associated with Schrödinger operators on the nilpotent Lie group
title_sort commutators associated with schrödinger operators on the nilpotent lie group
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5736795/
https://www.ncbi.nlm.nih.gov/pubmed/29290667
http://dx.doi.org/10.1186/s13660-017-1584-8
work_keys_str_mv AT nitianzhen commutatorsassociatedwithschrodingeroperatorsonthenilpotentliegroup
AT liuyu commutatorsassociatedwithschrodingeroperatorsonthenilpotentliegroup

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