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：Kajántó, Sándor[1]; Kristály, Alexandru[2,3]; Peter, Ioan Radu[4]; Zhao, Wei[5]

机构：[1] Department of Mathematics, Babe?-Bolyai University, Cluj-Napoca, Romania; [2] Department of Economics, Babe?-Bolyai University, Cluj-Napoca, Romania; [3] Institute of Applied Mathematics, Obuda University, Budapest, Hungary; [4] Department of Mathematics, Technical University of Cluj-Napoca, Memorandumului 28, Cluj-Napoca, RO-400114, Romania; [5] Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

年份：2023

外文期刊名：arXiv

收录：EI(收录号：20230098108)

语种：英文

外文关键词：Geometry

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. Copyright ? 2023, The Authors. All rights reserved.