Pointwise multipliers for Triebel–Lizorkin and Besov spaces on Lie groups

On a general Lie group G endowed with a sub-Riemannian structure and of local dimension d, we characterize the pointwise multipliers of Triebel–Lizorkin spaces F^α_{p,q} for p,q∈(1,∞) and α>d/p, and those of Besov spaces B^α_{p,q} for q∈[1,∞], p>d and d/p<1. When G is stratified, we extend the latter characterization to all p,q∈[1,∞] and α>d/p.