Algebra properties for Besov spaces on unimodular Lie groups

Joseph Feneuil (1)

1 IF - Institut Fourier

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

Mots clés: Besov spaces; unimodular Lie groups; algebra property

Domaines: Analyse fonctionnelle [math.FA]

Joseph Feneuil. Algebra properties for Besov spaces on unimodular Lie groups. 2015. ⟨hal-01167382⟩