An optimal improvement for the Hardy inequality on the hyperbolic space and related manifolds

DOI10.1017/prm.2018.139zbMath1457.46043arXiv1711.08423OpenAlexW2964175372WikidataQ128480592 ScholiaQ128480592MaRDI QIDQ3298555

Elvise Berchio, Debdip Ganguly, Gabriele Grillo, Yehuda Pinchover

Publication date: 14 July 2020

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.08423

zbMATH Keywords

hyperbolic spaceextremalsoptimal Hardy inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10) Potential theory on Riemannian manifolds and other spaces (31C12)

Related Items (17)

Hardy-Rellich and second order Poincaré identities on the hyperbolic space via Bessel pairs ⋮ Best Sobolev constants in the presence of sharp Hardy terms in Euclidean and hyperbolic space ⋮ \(L^p\) Hardy's identities and inequalities for Dunkl operators ⋮ Improved Poincaré-Hardy inequalities on certain subspaces of the Sobolev space ⋮ Sharp Morrey–Sobolev inequalities and eigenvalue problems on Riemannian–Finsler manifolds with nonnegative Ricci curvature ⋮ The abstract Birman-Schwinger principle and spectral stability ⋮ Optimal Hardy inequality for fractional Laplacians on the integers ⋮ Some functional properties on Cartan-Hadamard manifolds of very negative curvature ⋮ Optimal Hardy weights on the Euclidean lattice ⋮ Two-weight dyadic Hardy inequalities ⋮ Poincaré and Hardy Inequalities on Homogeneous Trees ⋮ New sharp Hardy and Rellich type inequalities on Cartan–Hadamard manifolds and their improvements ⋮ Improved multipolar Poincaré-Hardy inequalities on Cartan-Hadamard manifolds ⋮ On higher order Poincaré inequalities with radial derivatives and Hardy improvements on the hyperbolic space ⋮ Hardy-Poincaré-Sobolev type inequalities on hyperbolic spaces and related Riemannian manifolds ⋮ Universal Hardy–Sobolev inequalities on hypersurfaces of Euclidean space ⋮ Hardy's identities and inequalities on Cartan-Hadamard manifolds

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