On supercontractivity for Markov semigroups

DOI10.1007/s10114-005-0830-zzbMath1136.47030OpenAlexW2112882634MaRDI QIDQ2641557

Yong Hua Mao

Publication date: 20 August 2007

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

Full work available at URL: https://doi.org/10.1007/s10114-005-0830-z

zbMATH Keywords

Markov semigrouplogarithmic Sobolev inequalitycompact embeddingsupercontractivity

Mathematics Subject Classification ID

Related Items (1)

\(L^p\)-Poincaré inequality for general symmetric forms

Cites Work

• Ultracontractivity and the heat kernel for Schrödinger operators and Dirichlet Laplacians
• Analytic inequalities, isoperimetric inequalities and logarithmic Sobolev inequalities
• Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
• Relations between isoperimetry and spectral gap for finite Markov chains
• Logarithmic Sobolev inequality for symmetric forms
• Nash inequalities for general symmetric forms
• Ultracontractivity and Nash type inequalities
• Cheeger's inequalities for general symmetric forms and existence criteria for spectral gap.
• Functional inequalities for empty essential spectrum
• Functional inequalities for uniformly integrable semigroups and application to essential spectrums
• Hypercontractive Semigroups and Sobolev's Inequality
• Logarithmic Sobolev Inequalities
• Supercontractivity and ultracontractivity for (nonsymmetric) diffusion semigroups on manifolds
• Sobolev type inequalities for general symmetric forms
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