Improved Sobolev inequalities on groups of Iwasawa type in presence of symmetry

DOI10.1016/j.jmaa.2007.11.009zbMath1140.22007OpenAlexW2029033613MaRDI QIDQ2480331

Qiao-Hua Yang

Publication date: 31 March 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.11.009

zbMATH Keywords

Sobolev inequalitiesCayley transformHeisenberg type groupssimple Lie groups of real rank one

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Semisimple Lie groups and their representations (22E46) Nilpotent and solvable Lie groups (22E25) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Other special methods applied to PDEs (35A25)

Related Items (1)

Some weighted Hardy-type inequalities on anisotropic Heisenberg groups

Cites Work

• Sobolev inequalities with remainder terms
• A note on the Sobolev inequality
• Subelliptic estimates and function spaces on nilpotent Lie groups
• An approach to symmetric spaces of rank one via groups of Heisenberg type
• Nonlinear Liouville theorems for some critical problems on \(H\)-type groups.
• \(H\)-type groups and Iwasawa decompositions
• The Laplacian and the Kohn Laplacian for the sphere
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
• The Cayley transform and uniformly bounded representations
• Improved Sobolev inequalities on the Heisenberg group
• Sobolev spaces and the Cayley transform
• Extremals for the Sobolev Inequality on the Heisenberg Group and the CR Yamabe Problem
• Composition Series and Intertwining Operators for the Spherical Principal Series. II
• Composition Series and Intertwining Operators for the Spherical Principal Series. I

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