Fractional Poincaré and localized Hardy inequalities on metric spaces

Remarks about Hardy Inequalities on Metric Trees

where ψ > 0 is the so-called Hardy weight and C(Γ, ψ) is a positive constant which might depend on Γ and ψ, but which is independent of u. Evans, Harris and Pick [EHP] found a necessary and sufficient condition such that (1.1) holds for all functions u on Γ such that u(o) = 0 and such that the integral on the right hand side is finite. They consider even the case of non-symmetric Hardy weights....

Hardy Inequalities in Function Spaces

Hardy Inequalities for Fractional Integrals on General Domains

We prove a sharp Hardy inequality for fractional integrals for functions that are supported on a general domain. The constant is the same as the one for the half-space and hence our result settles a recent conjecture of Bogdan and Dyda [2].

Sharp Fractional Hardy Inequalities in Half-spaces Rupert L. Frank and Robert Seiringer

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces on half-spaces. Our proof relies on a non-linear and non-local version of the ground state representation.

Characterizations of Sobolev Inequalities on Metric Spaces

We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.