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

2016/05/09 by Tohru Ozawa, Michael Ruzhansky, Ozawa, Tohru +3
Computer Science · Mathematics · #22E30 #43A80 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1605.02520

openalex publication_date 2016/05/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 ℝⁿ our results provide new insights in view of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.

Citations

• Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups

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