Besov and Triebel--Lizorkin Spaces on Filtered Lie Groups with Polynomial Growth, I: Inclusions, Discretization, Duality

We continue to develop a theory of Besov and Triebel-Lizorkin spaces associated with weighted subcoercive operators on a real connected Lie group, specializing to the case of groups with polynomial volume growth. We consider the full scale of spaces and consider equivalent definitions, inclusions, discretization, and duality.