Molecular Decomposition of Besov Spaces Associated With Schrodinger Operators

Abstract

Recent work of Bui, Duong and Yan in [1] defined Besov spaces associated with a certain operator $L$ under the weak assumption that $L$ generates an analytic semigroup $e^{-tL}$ with Poisson kernel bounds on $L^2({\mathcal X})$ where ${\mathcal X}$ is a (possibly non-doubling) quasi-metric space of polynomial upper bound on volume growth. This note aims to extend Theorem 5.12 in [1], the decomposition of Besov spaces associated with Schrödinger operators, to more general $\alpha$, $p$, $q$.