Best constants for Moser-Trudinger inequalities, fundamental solutions and one-parameter representation formulas on groups of Heisenberg type
type: Item
instance of: scholarly article
title: Best constants for Moser-Trudinger inequalities, fundamental solutions and one-parameter representation formulas on groups of Heisenberg type
zbMATH Open document ID: 1011.22004
author: Guozhen Lu
author: William S. Cohn
publication date: 2003-04-10T00:00:00Z
review text: In the present paper, the authors derive fundamental solutions, representation formulas and a Moser-Trudinger inequality for Sobolev functions in the setting of groups of Heisenberg type. The problem of sharp constants in Moser-Trudinger inequalities is addressed.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 58E35
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 1885838
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Sobolev inequalities
zbMATH Keywords: Moser-Trudinger inequalities
zbMATH Keywords: best constants
zbMATH Keywords: fundamental solutions
reviewed by: Dumitru Motreanu
MaRDI profile type: Publication
full work available at URL: s101140200159
OpenAlex ID: W1999603929
cites work: A sharp inequality of J. Moser for higher order derivatives
cites work: Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
cites work: Sobolev inequalities, the Poisson semigroup, and analysis on the sphere Sn.
cites work: Q3756181
cites work: Extremals of functionals with competing symmetries
cites work: Competing symmetries, the logarithmic HLS inequality and Onofri's inequality on \(S^ n\)
cites work: Conformal deformations of metric on \({\mathcal S}\) 2
cites work: Estimates and extremals for zeta function determinants on four-manifolds
cites work: Extremal functions for the Trudinger-Moser inequality in 2 dimensions
cites work: Extremal functions for Moser’s inequality
cites work: Q5614914
cites work: Q5547919
cites work: On the positivity of the effective action in a theory of random surfaces
cites work: Sharp borderline Sobolev inequalities on compact Riemannian manifolds
cites work: Critical points of embeddings of \(H_ 0^{1,n}\) into Orlicz spaces
cites work: Best constants for Moser-Trudinger inequalities on the Heisenberg group
cites work: A fundamental solution for a subelliptic operator
cites work: Best constant in Sobolev inequality
cites work: Q3942008
cites work: Sharp constants in the Hardy-Littlewood-Sobolev and related inequalities
cites work: Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
cites work: The Yamabe problem on CR manifolds
cites work: Intrinsic CR normal coordinates and the CR Yamabe problem
cites work: Sharp inequalities and geometric manifolds
cites work: Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
cites work: Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
cites work: Geometric properties of Heisenberg-type groups
cites work: \(H\)-type groups and Iwasawa decompositions
cites work: Capacitary estimates and the local behavior of solutions of nonlinear subelliptic equations
cites work: Quasiregular maps on Carnot groups
cites work: Convolution operators and L(p, q) spaces
cites work: On the Grushin operator and hyperbolic symmetry
cites work: Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
cites work: Fundamental solution for the \(Q\)-Laplacian and sharp Moser--Trudinger inequality in Carnot groups.
cites work: Polar coordinates in Carnot groups
DOI: 10.1007/S101140200159
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 1885838