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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

Online
ISSN
1435-5337
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Volume 27, Issue 3

# An estimate on the heat kernel of Schrödinger operators with non-negative potentials on nilpotent Lie groups and its applications

Yu Liu
/ Jizheng Huang
/ Jianfeng Dong
Published Online: 2013-07-02 | DOI: https://doi.org/10.1515/forum-2012-0141

## Abstract

In this paper we investigate the heat kernel of the Schrödinger operator $L=-{\Delta }_{G}+W$ on the nilpotent Lie group G, where ΔG is the sub-Laplacian on G and the non-negative potential W belongs to the reverse Hölder class Bq1. The main aim of the paper is to give a pointwise estimate for the heat kernel of Schrödinger operators with non-negative potentials on the nilpotent Lie group G. As its applications, we obtain the Lp estimates for parabolic Schrödinger operators with certain non-negative potentials.

MSC: 22E30; 35J10; 32B30

Revised: 2013-04-06

Published Online: 2013-07-02

Published in Print: 2015-05-01

Funding Source: National Natural Science Foundation of China

Award identifier / Grant number: 10901018, 11001002

Funding Source: Fundamental Research Funds for the Central Universities

Award identifier / Grant number: J50101

Citation Information: Forum Mathematicum, Volume 27, Issue 3, Pages 1773–1798, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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