Existence of maximizers for Hardy-Littlewood-Sobolev inequalities on the Heisenberg group

DOI10.1512/iumj.2013.62.4976zbMath1299.39020arXiv1311.0094OpenAlexW2963900574MaRDI QIDQ5409838

Xiaolong Han

Publication date: 15 April 2014

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0094

zbMATH Keywords

Heisenberg groupHardy-Littlewood-Sobolev inequalityconcentration compactness principleexistence of maximizersbounds for sharp constants

Mathematics Subject Classification ID

Methods involving semicontinuity and convergence; relaxation (49J45) Functional inequalities, including subadditivity, convexity, etc. (39B62) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (8)

Reversed Hardy-Littlewood-Sobolev inequalities with weights on the Heisenberg group ⋮ Integral inequalities with an extended Poisson kernel and the existence of the extremals ⋮ Existence of extremal functions for the Stein-Weiss inequalities on the Heisenberg group ⋮ Sharp Hardy-Littlewood-Sobolev inequalities on quaternionic Heisenberg groups ⋮ Reverse Stein-Weiss inequalities on the upper half space and the existence of their extremals ⋮ Existence of extremals of Dunkl-type Sobolev inequality and of Stein-Weiss inequality for Dunkl Riesz potential ⋮ Reverse Stein–Weiss inequalities and existence of their extremal functions ⋮ Hardy-Littlewood-Sobolev inequalities with the fractional Poisson kernel and their applications in PDEs

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