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arXiv · 1505.06991

Algebra properties for Besov spaces on unimodular Lie groups

Joseph Feneuil
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Abstract

We consider the Besov space $B^{p,q}_\alpha(G)$ 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 $B^{p,q}_\alpha(G) \cap L^\infty(G)$ for $\alpha>0$, $1\leq p\leq+\infty$ and $1\leq q\leq +\infty$. These results hold for polynomial as well as for exponential volume growth of balls.

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Joseph Feneuil. 2015-05-26. Algebra properties for Besov spaces on unimodular Lie groups. https://arxiv.org/abs/1505.06991

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