文献类型：期刊文献

英文题名：A generic functional inequality and Riccati pairs: an alternative approach to Hardy-type inequalities

作者：Kajanto, Sandor[1];Kristaly, Alexandru[2,3];Peter, Ioan Radu[4];Zhao, Wei[5]

机构：[1]Babes Bolyai Univ, Dept Math, Cluj Napoca, Romania;[2]Babes Bolyai Univ, Dept Econ, Cluj Napoca, Romania;[3]Obuda Univ, Inst Appl Math, Budapest, Hungary;[4]Tech Univ Cluj Napoca, Dept Math, Str Memorandumului 28, RO-400114 Cluj Napoca, Romania;[5]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2024

卷号：390

期号：3

起止页码：3621

外文期刊名：MATHEMATISCHE ANNALEN

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001194592900002)】；

基金：The authors thank the anonymous Referees for their valuable comments and suggestions that significantly improved the presentation of the manuscript.

语种：英文

外文关键词：26D10; 58J05; 58J60; 35A23; 49R05; 46E35

摘要：We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known and genuinely new Hardy-type inequalities. For the additive version, we introduce Riccati pairs that extend Bessel pairs developed by Ghoussoub and Moradifam (Proc. Natl. Acad. Sci. USA, 2008 & Math. Ann., 2011). This concept enables us to give very short/elegant proofs of a number of celebrated functional inequalities on Riemannian manifolds with sectional curvature bounded from above by simply solving a Riccati-type ODE. Among others, we provide alternative proofs for Caccioppoli inequalities, Hardy-type inequalities and their improvements, spectral gap estimates, interpolation inequalities, and Ghoussoub-Moradifam-type weighted inequalities. Concerning the multiplicative form, we prove sharp uncertainty principles on Cartan-Hadamard manifolds, i.e., Heisenberg-Pauli-Weyl uncertainty principles, Hydrogen uncertainty principles and Caffarelli-Kohn-Nirenberg inequalities. Some sharpness and rigidity phenomena are also discussed.