Some Hardy Inequalities on the Heisenberg Group

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Hardy-type inequalities related to degenerate elliptic differential operators (2006, background): “der terms for inequality (2.28). The reader interested in the study of Hardy inequalities with remainder terms can refer to [4, 5, 10, 11, 31] and the references therein for the Euclidean case and to [19] for the case ∇L = ∇H, the Heisenberg gradient on the Heisenberg group. Proof of Theorem 2.7. We”
Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group (2015, background): “o be used with the same meaning in the literature) fractional powers of the sublaplacian L on the Heisenberg group Hn. Some Hardy inequalities are already known for the sublaplacian, see for instance [2, 22, 5], and also the very recent work by P. Ciatti, 2010 Mathematics Subject Classiﬁcation. Prim”
On horizontal Hardy, Rellich, Caffarelli–Kohn–Nirenberg and p-sub-Laplacian inequalities on stratified groups (2016, background): “again with p N−p being the best constant (see [11] and [48] for the version on the Heisenberg group).”