Hardy inequalities with non-standard remainder terms

By Andrea Cianchi, A. Ferone. 2008

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Scale invariance structures of the critical and the subcritical Hardy inequalities and their improvements (2017, background): “Another type of remainder term expressed by a distance from the set of virtual extremals was obtained (see [8,20]).”
Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for ^{}-weighted Hardy inequalities (2017, background): “ved that there exists no strictly positive function V ∈ C1(0,∞) such that the inequality Z Rn |∇f|2dx ≥ n− 2 2 2Z Rn |f|2 |x|2 dx+ Z Rn V(|x|)|f|2dx holds for any f ∈ W1,2(Rn). Cianchi and Ferone [CF08] showed that for all 1 < p < n there exists a constant C = C(p,n) such that Z Rn |∇f|pdx ≥”