Algebra properties for Besov spaces on unimodular Lie groups

Joseph Feneuil

Algebra properties for Besov spaces on unimodular Lie groups

Analysis of PDEs 2015-05-27 v1

Authors: Joseph Feneuil

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.

Keywords

Besov spaces unimodular Lie groups sublaplacian heat kernel estimates algebra property volume growth

Cite

@article{arxiv.1505.06991,
  title  = {Algebra properties for Besov spaces on unimodular Lie groups},
  author = {Joseph Feneuil},
  journal= {arXiv preprint arXiv:1505.06991},
  year   = {2015}
}