Algebra properties for Besov spaces on unimodular Lie groups

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 $B^{p,q}_α(G) \cap L^\infty(G)$ for $α>0$, $1\leq p\leq+\infty$ and $1\leq q\leq +\infty$. These results hold for polynomial as well as for exponential volume growth of balls.

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