Recent work of Bui, Duong and Yan in  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 L²(X) where X is a (possibly non-doubling) quasimetric space of polynomial upper bound on volume growth. This note aims to extend certain results in  to a more general setting when the underlying space can have different dimensions at 0 and infinity. For example, we make some extensions to the Besov norm equivalence result in Proposition 4.4 of , such as to more general class of functions with suitable decay at 0 and infinity, and to non-integer k ≥ 1.
|Number of pages||16|
|Journal||Communications in Mathematical Analysis|
|Publication status||Published - 2014|
- Analytic semigroup
- Besov space
- Embedding theorem
- Heat kernel