Generalized Schrödinger operators on the Heisenberg group and Hardy spaces

The Anh Bui; Qing Hong; Guorong Hu

doi:10.1016/j.jfa.2024.110399

Generalized Schrödinger operators on the Heisenberg group and Hardy spaces

The Anh Bui, Qing Hong, Guorong Hu^*

^*Corresponding author for this work

School of Mathematical and Physical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

Let L=−Δ_Hⁿ+μ be a generalized Schrödinger operator on the Heisenberg group Hⁿ, where Δ_Hⁿ is the sub-Laplacian, and μ is a nonnegative Radon measure satisfying certain conditions. In this paper, we first establish some estimates of the fundamental solution and the heat kernel of L. Applying these estimates, we then study the Hardy spaces H_L¹(Hⁿ) introduced in terms of the maximal function associated with the heat semigroup e^−tL; in particular, we obtain an atomic decomposition of H_L¹(Hⁿ), and prove the Riesz transform characterization of H_L¹(Hⁿ). The dual space of H_L¹(Hⁿ) is also studied.

Original language	English
Article number	110399
Pages (from-to)	1-53
Number of pages	53
Journal	Journal of Functional Analysis
Volume	286
Issue number	10
DOIs	https://doi.org/10.1016/j.jfa.2024.110399
Publication status	Published - 15 May 2024

Keywords

Hardy space
Heisenberg group
Schrödinger operator

Access to Document

10.1016/j.jfa.2024.110399

Cite this

@article{5e24d0bcfc0c4613bca8cd0db54284fc,

title = "Generalized Schr{\"o}dinger operators on the Heisenberg group and Hardy spaces",

abstract = "Let L=−ΔHn+μ be a generalized Schr{\"o}dinger operator on the Heisenberg group Hn, where ΔHn is the sub-Laplacian, and μ is a nonnegative Radon measure satisfying certain conditions. In this paper, we first establish some estimates of the fundamental solution and the heat kernel of L. Applying these estimates, we then study the Hardy spaces HL1(Hn) introduced in terms of the maximal function associated with the heat semigroup e−tL; in particular, we obtain an atomic decomposition of HL1(Hn), and prove the Riesz transform characterization of HL1(Hn). The dual space of HL1(Hn) is also studied.",

keywords = "Hardy space, Heisenberg group, Schr{\"o}dinger operator",

author = "Bui, {The Anh} and Qing Hong and Guorong Hu",

year = "2024",

month = may,

day = "15",

doi = "10.1016/j.jfa.2024.110399",

language = "English",

volume = "286",

pages = "1--53",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Elsevier",

number = "10",

}

TY - JOUR

T1 - Generalized Schrödinger operators on the Heisenberg group and Hardy spaces

AU - Bui, The Anh

AU - Hong, Qing

AU - Hu, Guorong

PY - 2024/5/15

Y1 - 2024/5/15

N2 - Let L=−ΔHn+μ be a generalized Schrödinger operator on the Heisenberg group Hn, where ΔHn is the sub-Laplacian, and μ is a nonnegative Radon measure satisfying certain conditions. In this paper, we first establish some estimates of the fundamental solution and the heat kernel of L. Applying these estimates, we then study the Hardy spaces HL1(Hn) introduced in terms of the maximal function associated with the heat semigroup e−tL; in particular, we obtain an atomic decomposition of HL1(Hn), and prove the Riesz transform characterization of HL1(Hn). The dual space of HL1(Hn) is also studied.

AB - Let L=−ΔHn+μ be a generalized Schrödinger operator on the Heisenberg group Hn, where ΔHn is the sub-Laplacian, and μ is a nonnegative Radon measure satisfying certain conditions. In this paper, we first establish some estimates of the fundamental solution and the heat kernel of L. Applying these estimates, we then study the Hardy spaces HL1(Hn) introduced in terms of the maximal function associated with the heat semigroup e−tL; in particular, we obtain an atomic decomposition of HL1(Hn), and prove the Riesz transform characterization of HL1(Hn). The dual space of HL1(Hn) is also studied.

KW - Hardy space

KW - Heisenberg group

KW - Schrödinger operator

UR - http://www.scopus.com/inward/record.url?scp=85188242763&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2024.110399

DO - 10.1016/j.jfa.2024.110399

M3 - Article

AN - SCOPUS:85188242763

SN - 0022-1236

VL - 286

SP - 1

EP - 53

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 10

M1 - 110399

ER -

Generalized Schrödinger operators on the Heisenberg group and Hardy spaces

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this