Muckenhoupt Ap-properties of Distance Functions and Applications to Hardy–Sobolev -type Inequalities
By Bartłomiej Dyda, L. Ihnatsyeva, Juha Lehrbäck, Heli Tuominen, Antti V. Vahakangas. 2017
57 citations recorded by the source corpus.
Let X be a metric space equipped with a doubling measure. We consider weights w(x) = dist(x,E)−α, where E is a closed set in X and α∈ℝ$\alpha \in \mathbb {R}$. We establish sharp conditions, based on the Assouad (co)dimension of E, for the inclusion of w in Muckenhoupt’s Ap classes of weights, 1 ≤ p < ∞. With the help of general Ap-weighted embedding results, we then prove (global) Hardy–Sobolev inequalities and also fractional versions of such inequalities in the setting of metric spaces.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/81ad7309c342b69333dd6295be7a420e07efffa6
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In Applied Mathematics
Citations in the corpus
- Assouad Dimension and Fractal Geometry (2020, background): “Finally, connections between the Assouad dimension and Muckenhoupt weights are given in [58], see also [187].”