Sharp Hardy-Littlewood-Sobolev inequalities on quaternionic Heisenberg groups

DOI10.1016/j.na.2015.10.018zbMath1329.26028arXiv1407.3417OpenAlexW2952304212MaRDI QIDQ898376

An Zhang, Michael Christ, He Ping Liu

Publication date: 8 December 2015

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.3417

zbMATH Keywords

conformal symmetryextremizersHardy-Littlewood-Sobolev inequalitiesquaternionic Heisenberg group

Mathematics Subject Classification ID

Inequalities involving derivatives and differential and integral operators (26D10) Sub-Riemannian geometry (53C17) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23) Harmonic analysis and PDEs (42B37)

Related Items (11)

\(L^p\) joint eigenfunction bounds on quaternionic spheres ⋮ Cauchy–Szegö commutators on weighted Morrey spaces ⋮ Hardy–Littlewood–Sobolev inequality and existence of the extremal functions with extended kernel ⋮ Existence of extremal functions for the Stein-Weiss inequalities on the Heisenberg group ⋮ Sharp reversed Hardy–Littlewood–Sobolev inequality with extension kernel ⋮ Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group ⋮ The optimal constant in the \(L^2\) Folland-Stein inequality on the H-type group ⋮ The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds ⋮ Sharp Hardy-Littlewood-Sobolev inequalities on a class of H-type groups ⋮ An explicit formula of Cauchy-Szego kernel for quaternionic Siegel upper half space and applications ⋮ Sharp Hardy-Littlewood-Sobolev inequalities on the octonionic Heisenberg group

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