The sharp higher order Hardy--Rellich type inequalities on the homogeneous groups

2017/08/30 by Van Hoang Nguyen, Nguyen, Van Hoang
Mathematics · #22E30 #26D10 #43A80 #43A85 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1708.09311

openalex publication_date 2017/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove several interesting equalities for the integrals of higher order derivatives on the homogeneous groups. As consequences, we obtain the sharp Hardy--Rellich type inequalities for higher order derivatives including both the subcritical and critical inequalities on the homogeneous groups. We also prove several uncertainty principles on the homogeneous groups. Our results seem to be new even in the case of Euclidean space \mathbb Rⁿ and give a simple proof of several classical Hardy--Rellich type inequalities in \mathbb Rⁿ.

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