Peer-reviewedCC BY 4.0Colloquium Mathematicum
Algebra properties for Besov spaces on unimodular Lie groups
Abstract
We consider the Besov space Bp,qα(G) on a unimodular Lie group G equipped with a sublaplacian Δ. Using estimates of the heat kernel associated with Δ, we give several characterizations of Besov spaces, and show an algebra property for Bp,qα(G) for α>0, 1≤ p,q ≤ +∞. These results hold for polynomial as well as for exponential volume growth of balls.
Related
- Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups, III: the Spaces F∞,qα
- Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups, II: Pointwise Multiplication, Localization, Differences
- Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups with Polynomial Growth, I: Inclusions, Discretization, Duality
- Besov and Triebel-Lizorkin Spaces on Filtered Lie Groups with Polynomial Growth, II: Interpolation, Localization, Pointwise Multiplication
- Prevalent smoothness in inhomogeneous Besov spaces
BibTeX
@article{feneuil2026algebra,
title = {{Algebra properties for Besov spaces on unimodular Lie groups}},
author = {Joseph Feneuil},
journal = {Colloquium Mathematicum},
year = {2026},
month = oct,
doi = {10.4064/cm6649-12-2017},
eprint = {1505.06991},
archivePrefix = {arXiv},
url = {https://hal.science/hal-01167382v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Algebra properties for Besov spaces on unimodular Lie groups
AU - Joseph Feneuil
PY - 2026
DA - 2026/10/12
JO - Colloquium Mathematicum
DO - 10.4064/cm6649-12-2017
UR - https://hal.science/hal-01167382v2
AB - We consider the Besov space B^p,q_α(G) on a unimodular Lie group G equipped with a sublaplacian Δ. Using estimates of the heat kernel associated with Δ, we give several characterizations of Besov spaces, and show an algebra property for B^p,q_α(G) for α>0, 1≤ p,q ≤ +∞. These results hold for polynomial as well as for exponential volume growth of balls.
ER -