  We study non-local or fractional capacities in metric measure spaces. Our
main goal is to clarify the relations between relative Hajlasz-Triebel-Lizorkin
capacities, potentional Triebel-Lizorkin capacities, and metric space variants
of Riesz capacities. As an application of our results, we obtain a
characterization of a Hajlasz-Triebel-Lizorkin capacity density condition,
which is based on an earlier characterization of a Riesz capacity density
condition in terms of Hausdorff contents.
