Algebra properties for Besov spaces on unimodular Lie groups
Volume 154 / 2018
Colloquium Mathematicum 154 (2018), 205-240
MSC: Primary 46E35; Secondary 43A15, 35S50.
DOI: 10.4064/cm6649-12-2017
Published online: 10 September 2018
Abstract
We consider the Besov space $B^{p,q}_\alpha (G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $\varDelta $. Using estimates of the heat kernel associated with $\varDelta $, we give several characterizations of Besov spaces, and show an algebra property for $B^{p,q}_\alpha (G) \cap L^\infty (G)$ when $\alpha \gt 0$ and $1\leq p,q\leq \infty $. These results hold for polynomial as well as for exponential volume growth of balls.
