55 citations · 230 across the 22 of their papers we have counts for
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Fractional Poincaré and localized Hardy inequalities on metric spaces
Bartłomiej Dyda, Juha Lehrbäck, Antti V. Vähäkangas
We prove fractional Sobolev-Poincaré inequalities, capacitary versions of fractional Poincaré inequalities, and pointwise and localized fractional Hardy inequalities in a metric sp…
Fractional Hardy-Sobolev type inequalities for half spaces and John domains
Bartłomiej Dyda, Juha Lehrbäck, Antti V. Vähäkangas
As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina…
Muckenhoupt -properties of distance functions and applications to Hardy-Sobolev -type inequalities
Bartłomiej Dyda, Lizaveta Ihnatsyeva, Juha Lehrbäck +2
Let be a metric space equipped with a doubling measure. We consider weights , where is a closed set in and . We estab…
On improved fractional Sobolev-Poincaré inequalities
Bartłomiej Dyda, Lizaveta Ihnatsyeva, Antti V. Vähäkangas
We prove a certain improved fractional Sobolev-Poincaré inequality on John domains; the proof is based on the equivalence of the corresponding weak and strong type inequalities. We…
Characterizations for fractional Hardy inequality
Bartłomiej Dyda, Antti V. Vähäkangas
We provide a Maz'ya type characterization for a fractional Hardy inequality. As an application, we show that a bounded open set admits a fractional Hardy inequality if and only…
A framework for fractional Hardy inequalities
Bartłomiej Dyda, Antti V. Vähäkangas
We provide a general framework for fractional Hardy inequalities. Our framework covers, for instance, fractional inequalities related to the Dirichlet forms of some Lévy processes,…