Molecular decomposition of Besov spaces associated with Schrödinger operators

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(X) where X is a (possibly non-doubling) quasimetric 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 α, p, q.