Algebra properties for Besov spaces on unimodular Lie groups

Abstract

We consider the Besov space $B_{\alpha }^{p,q}(G)$ on a unimodular Lie group $G$ equipped with a sublaplacian $\Delta$. Using estimates of the heat kernel associated with $\Delta$, we give several characterizations of Besov spaces, and show an algebra property for $B_{\alpha }^{p,q}(G)\cap L^{\infty }(G)$ for $\alpha >0$, $1\le p\le +\infty$ and $1\le q\le +\infty$. These results hold for polynomial as well as for exponential volume growth of balls.

29 pages