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

Authors

Fabrice Baudoin, Univ Connecticut, Dept Math, Storrs, CT 06269 USAFollow
Li Chen, Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USAFollow

Author ORCID Identifier

Chen, Li https://orcid.org/0000-0002-9508-3368

Document Type

Article

Publication Date

3-2022

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) over tilde (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.

Publication Source (Journal or Book title)

ARCHIV DER MATHEMATIK

First Page

291

Last Page

304

Recommended Citation

Baudoin, F., & Chen, L. (2022). A note on second order Riesz transforms in 3-dimensional Lie groups. ARCHIV DER MATHEMATIK, 118 (3), 291-304. https://doi.org/10.1007/s00013-021-01699-6