2023/10/10 by Anh Xuan, Do, Anh Xuan, Nguyen Lam +3
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2310.06637
openalex publication_date 2023/10/10 · openalex created_date 2023/10/12 · openalex updated_date 2026/07/28
We investigate necessary and sufficient conditions on the weights for the Hardy-Rellich inequalities to hold, and propose a new way to use the notion of Bessel pair to establish the optimal Hardy-Rellich type inequalities. Our results sharpened earlier Hardy-Rellich and Rellich type inequalities in the literature. We also study several results about the symmetry and symmetry breaking properties of the Rellich type and Hardy-Rellich type inequalities, and then partially answered an open question raised by Ghoussoub and Moradifam. Namely, we will present conditions on the weights such that the Rellich type and Hardy-Rellich type inequalities hold for all functions if and only if the same inequalities hold for all radial functions.