A class of Caffarelli-Kohn-Nirenberg type inequalities on the \(H\)-type group

DOI10.4171/RSMUP/132-13zbMath1320.46037OpenAlexW2021373093MaRDI QIDQ481038

Jingbo Dou, Shu Tao Zhang, Ya Zhou Han

Publication date: 12 December 2014

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/rsmup/132-13

zbMATH Keywords

\(H\)-type groupCaffarelli-Kohn-Nirenberg type inequalityHardy-Sobolev-type inequality

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Analysis on real and complex Lie groups (22E30) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (9)

Several logarithmic Caffarelli-Kohn-Nirenberg inequalities and applications ⋮ Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and \(p\)-sub-Laplacian systems ⋮ Caffarelli–Kohn–Nirenberg inequalities on Lie groups of polynomial growth ⋮ Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for 𝐿^{𝑝}-weighted Hardy inequalities ⋮ Local behavior of solutions to subelliptic problems with Hardy potential on Carnot groups ⋮ Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups ⋮ Sharp Caffarelli-Kohn-Nirenberg-type inequalities on Carnot groups ⋮ Hardy, weighted Trudinger-Moser and Caffarelli-Kohn-Nirenberg type inequalities on Riemannian manifolds with negative curvature ⋮ Critical problems with Hardy potential on stratified Lie groups

Cites Work

• Unnamed Item
• Unnamed Item
• A Sobolev-Hardy inequality with applications to a nonlinear elliptic equation arising in astrophysics
• Polar coordinates on \(H\)-type groups and applications
• Minimizers of Caffarelli-Kohn-Nirenberg inequalities with the singularity on the boundary
• Hardy inequalities and some critical elliptic and parabolic problems
• Polar coordinates in Carnot groups
• Regularity near the characteristic set in the nonlinear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups.
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type
• On first order interpolation inequalities with weights on the Heisenberg group
• Hardy-Sobolev type inequalities on the H-type group
• Sobolev Interpolation Inequalities with Weights
• A unified approach to improved $L^p$ Hardy inequalities with best constants
• Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents

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