A fractional order Hardy inequality

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A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations (2015, background): “timate the interpolation error. In order to achieve this, it is convenient to understand the relation between the norm in V, and the (semi)norm in Hs(Ω). Proposition 2.5 (Hardy-type inequalities, see [25, 18]). Let Ω be as above. If 0 <s<1 2, then there exists c= c(Ω,n,s) >0 such that (2.3)”
The best constant in a fractional Hardy inequality (2008, methodology): “This is observed in [14] ([16] gives a direct counterexample).”
The second eigenvalue of the fractional p-Laplacian (2014, background): “Ω |un(x)− un(y)| |x− y|N+s p dx dy = 0, see for example the counterexample contained in [11] at page 557.”
A framework for fractional Hardy inequalities (2013, methodology): “a refinement of the techniques in [7] where, e.”
The fractional Cheeger problem (2013, unknown): “Ω |u(x)|p δΩ(x) p dx ≤ C ′ ( [u]pW s,p(Ω) + ‖u‖ p Lp(Ω) ) , u ∈ C∞ 0 (Ω), with C ′ = C ′(N, s, p,Ω), see [13].”
Hardy inequalities for fractional integrals on general domains (2009, unknown): “For 0 < p ≤ 1 the inequality continuous to hold (see [5]), however, the sharp constant is not known.”
Sharp Fractional Hardy Inequalities in Half-Spaces (2009, methodology): “We refer to [4, 6, 8] and the references therein for motivations and applications of fractional Hardy inequalities.”