Fractional Hardy inequalities in doubling metric measure spaces self-improve in both the power p and the regularity theta, via an equivalence with Hardy inequalities in hyperbolic fillings.
Classifying Triebel-Lizorkin capacities in metric spaces
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abstract
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.
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Self-improvement of fractional Hardy inequalities in metric measure spaces via hyperbolic fillings
Fractional Hardy inequalities in doubling metric measure spaces self-improve in both the power p and the regularity theta, via an equivalence with Hardy inequalities in hyperbolic fillings.