$L^p$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups

Abstract

We prove $L^p$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already in the abelian case of ${\mathbb{R}}^n$ our results provide new insights in view of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.

12 pages; a revised version. arXiv admin note: text overlap with arXiv:1603.06239

References in corpus (3)

• Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups
• On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and $p$-sub-Laplacian inequalities on stratified groups
• Layer potentials, Green's formulae, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

Cited by in corpus (6)

• On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and $p$-sub-Laplacian inequalities on stratified groups
• Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups
• Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for $L^p$-weighted Hardy inequalities
• The sharp higher order Hardy--Rellich type inequalities on the homogeneous groups
• Weighted $L^p$-Hardy and $L^p$-Rellich inequalities with boundary terms on stratified Lie groups
• Finsler Hardy inequalities