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Algebra properties for Besov spaces on unimodular Lie groups

Volume 154 / 2018

Joseph Feneuil Colloquium Mathematicum 154 (2018), 205-240 MSC: Primary 46E35; Secondary 43A15, 35S50. DOI: 10.4064/cm6649-12-2017 Published online: 10 September 2018

Abstract

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

Authors

  • Joseph FeneuilSchool of Mathematics
    University of Minnesota
    206 Church St. SE
    Minneapolis, MN 55455, U.S.A.
    Current address:
    Department of Mathematics
    Temple University
    1805 N Broad St.
    Philadelphia, PA 19122, U.S.A.
    e-mail
    e-mail

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