Nash inequalities for Markov processes in dimension one

DOI10.1007/s101140100128zbMath1022.60074OpenAlexW2005675097MaRDI QIDQ1601228

Young Hua Mao

Publication date: 27 October 2003

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s101140100128

zbMATH Keywords

diffusion processbirth-death processHardy type inequalityNash inequalities

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Diffusion processes (60J60) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (13)

Criteria for super- and weak-Poincaré inequalities of ergodic birth-death processes ⋮ Discrete Hardy-type Inequalities ⋮ Discrete weighted Hardy inequalities with different kinds of boundary conditions ⋮ Speed of stability for birth-death processes ⋮ The optimal constant in generalized Hardy's inequality ⋮ Bilateral Hardy-type inequalities ⋮ Variational formulas of Poincaré-type inequalities for birth-death processes. ⋮ Polynomial convergence for reversible jump processes ⋮ \(L^2\)-decay rate for non-ergodic Jackson network ⋮ Mixed eigenvalues of discrete \(p\)-Laplacian ⋮ Dual ultracontractivity and its applications ⋮ \(L^p\)-Poincaré inequality for general symmetric forms ⋮ Capacitary criteria for Poincaré-type inequalities

Cites Work

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• Hardy-Littlewood theory for semigroups
• Upper bounds for symmetric Markov transition functions
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Nash inequalities for general symmetric forms
• Analytic proof of dual variational formula for the first eigenvalue in dimension one
• Sobolev inequalities in disguise

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