Bessel pairs and optimal Hardy and Hardy–Rellich inequalities

By Nassif Ghoussoub, Amir Moradifam. 2011

189 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f7c39ce43dae0043bdc9a99d4c01897fa8ea34d3

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In Applied Mathematics

Citations in the corpus

Sharp uncertainty principles on Riemannian manifolds: the influence of curvature (2013, background): “Adimurthi, Chaudhuri and Ramaswamy [1], Barbatis, Filippas and Tertikas [5], Brezis and Vázquez [8], Filippas and Tertikas [20], Ghoussoub and Moradifam [22, 23], Wang and Willem [36], etc.”
Sharp Poincar\'e-Hardy and Poincar\'e-Rellich inequalities on the hyperbolic space (2015, methodology): “= (N− 1)2/4. Rellich inequalities in the Euclidean setting go back to [37], and a number of reﬁnement and improvements have been given till quite recently, see e.g. without any claim for completeness [6, 12, 16, 22, 23, 33, 39]. The very recent paper [32] proposed a method of proof involving a decom”
Hardy-Poincaré, Rellich and uncertainty principle inequalities on Riemannian manifolds (2011, unknown): “[2], [10], [6], [1], [3], [12], [8], [13] and the references therein.”
Mathematical Analysis of Partial Differential Equations Modeling Electrostatic MEMS (2010, methodology): “They rely on the results of Ghoussoub-Moradifam in [84], which provide necessary and sufficient conditions for such inequalities to hold.”
Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for ^{}-weighted Hardy inequalities (2017, background): “p (a+b|x|α) β p |x|m+1 f Lp(Rn) ≤ (a+b|x|α) β p |x|m ∇f Lp(Rn) (1.17) with the sharp constant for n 6= pm+p−αβ. The L2-version, that is, when p = 2 the inequalities (1.16) and (1.17) were obtained in [GM11]. We also shall note that these CKN, REMAINDERS AND SUPERWEIGHTS FOR Lp-WEIGHTED HARDY INEQUAL”