A note on second order Riesz transforms in 3-dimensional Lie groups

Fabrice Baudoin; Li Chen

doi:10.1007/s00013-021-01699-6

A note on second order Riesz transforms in 3-dimensional Lie groups

^*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

Abstract

We prove explicit L^p bounds for second order Riesz transforms of the sub-Laplacian and of the Laplacian in the Lie groups H, SU(2) , and SL~ (2). Our proof makes use of martingale transform techniques and specific commutation properties between the complex gradient and the sub-Laplacian in those Lie groups.

Original language	English
Journal	ARCHIV DER MATHEMATIK
Volume	118
Issue	3
Pages (from-to)	291-304
Number of pages	14
ISSN	0003-889X
DOIs	https://doi.org/10.1007/s00013-021-01699-6
Publication status	Published - Mar 2022
Externally published	Yes

Keywords

3- dimensional Lie groups
Elliptic Laplacian
Heisenberg groups
Martingale transform
Second order Riesz transforms
Sub-Laplacian

Access to Document

10.1007/s00013-021-01699-6

Cite this

@article{b5151df8786442159046ca39cbf5b616,

title = "A note on second order Riesz transforms in 3-dimensional Lie groups",

abstract = "We prove explicit Lp bounds for second order Riesz transforms of the sub-Laplacian and of the Laplacian in the Lie groups H, SU(2) , and SL~ (2). Our proof makes use of martingale transform techniques and specific commutation properties between the complex gradient and the sub-Laplacian in those Lie groups.",

keywords = "3- dimensional Lie groups, Elliptic Laplacian, Heisenberg groups, Martingale transform, Second order Riesz transforms, Sub-Laplacian",

author = "Fabrice Baudoin and Li Chen",

note = "Publisher Copyright: {\textcopyright} 2022, Springer Nature Switzerland AG.",

year = "2022",

month = mar,

doi = "10.1007/s00013-021-01699-6",

language = "English",

volume = "118",

pages = "291--304",

journal = "ARCHIV DER MATHEMATIK",

issn = "0003-889X",

publisher = "Birkhauser Verlag Basel",

number = "3",

}

TY - JOUR

T1 - A note on second order Riesz transforms in 3-dimensional Lie groups

AU - Baudoin, Fabrice

AU - Chen, Li

PY - 2022/3

Y1 - 2022/3

N2 - We prove explicit Lp bounds for second order Riesz transforms of the sub-Laplacian and of the Laplacian in the Lie groups H, SU(2) , and SL~ (2). Our proof makes use of martingale transform techniques and specific commutation properties between the complex gradient and the sub-Laplacian in those Lie groups.

AB - We prove explicit Lp bounds for second order Riesz transforms of the sub-Laplacian and of the Laplacian in the Lie groups H, SU(2) , and SL~ (2). Our proof makes use of martingale transform techniques and specific commutation properties between the complex gradient and the sub-Laplacian in those Lie groups.

KW - 3- dimensional Lie groups

KW - Elliptic Laplacian

KW - Heisenberg groups

KW - Martingale transform

KW - Second order Riesz transforms

KW - Sub-Laplacian

UR - http://www.scopus.com/inward/record.url?scp=85124515579&partnerID=8YFLogxK

U2 - 10.1007/s00013-021-01699-6

DO - 10.1007/s00013-021-01699-6

M3 - Journal article

AN - SCOPUS:85124515579

SN - 0003-889X

VL - 118

SP - 291

EP - 304

JO - ARCHIV DER MATHEMATIK

JF - ARCHIV DER MATHEMATIK

IS - 3

ER -

A note on second order Riesz transforms in 3-dimensional Lie groups

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this