Limiting embedding theorems forWs,p whens ↑ 1 and applications

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Fractional Caffarelli–Kohn–Nirenberg inequalities (2017, unknown): “In the case 0 < p < d , one has, for 1 / 2 < s < 1 (see [7]), The same proof yields, with α 1 = α 2 = α = 0, σ > − s , and 1 /τ + γ/d > 0, Using the results in [2,3], one knows that lim s → 1 We then derive that Remark 2.4.”
Sharp Fractional Hardy Inequalities in Half-Spaces (2009, methodology): “[BBM] J. Bourgain, H. Brezis, P. Mironescu, Limiting embedding theorems for W s,p when s ↑ 1 and applications.”
Pitt's inequality and the fractional Laplacian: Sharp error estimates (2007, methodology): “RC/ i2 CD˛ 2 n=2 .n 2 / Z RC RC jg.t/ g.s/j2 ˛;n.t=s/ dt t ds s (3.6) where ˛;n.t/ D Z Sn 1 jt C 1 t 2 1j .nC˛/=2 d and C˛ D ˛ n ˛ 4 . nC ˛ 4 2 ; D˛ D n=2 ˛ ˛ 4 .nC˛ 2 / .2 ˛ 2 / C˛: The classical Aronszajn–Smith representation formula for the fractional Laplacian combined with the Hardy–Littlewood–”
On weighted Poincar\'e inequalities (2012, unknown): “For any such a weight φ there exists a positive, non-zero σ-finite Borel measure ν on ((1) 2 , 1], such that (1) φ(x) = ˆ 1 ρ(x,x0)∨1/2 ν(dt) = ˆ 1 1/2 χBt(x) ν(dt), x ∈ B1 \B1/2.”
Anisotropic fractional perimeters (2013, unknown): “Fractional s -perimeters have attracted increased attention in recent years (see [3, 6–8, 11, 14, 15, 36] and the references therein).”