Criteria for the super-Poincare inequality and the weak-Pincare inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 ...Criteria for the super-Poincare inequality and the weak-Pincare inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 （p. 15） of Prof. Mu-Fa Chen＇s book ＂Eigenvalues, Inequalities and Ergodic展开更多
By establishing the intrinsic super-Poincar'e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive.These con...By establishing the intrinsic super-Poincar'e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive.These conditions,as well as the resulting uniform upper bounds on the intrinsic heat kernels,are sharp for some concrete examples.展开更多
Poincaréinequality has been studied by Bobkov for radial measures,but few are known about the logarithmic Sobolev inequality in the radial case.We try to fill this gap here using different methods:Bobkov's ar...Poincaréinequality has been studied by Bobkov for radial measures,but few are known about the logarithmic Sobolev inequality in the radial case.We try to fill this gap here using different methods:Bobkov's argument and super-Poincaréinequalities,direct approach via L_(1)-logarithmic Sobolev inequalities.We also give various examples where the obtained bounds are quite sharp.Recent bounds obtained by Lee–Vempala in the log-concave bounded case are refined for radial measures.展开更多
基金Supported by Natural Science Foundation of Fujian Province(Grant No.2010J05002)
文摘Criteria for the super-Poincare inequality and the weak-Pincare inequality about ergodic birth-death processes are presented. Our work further completes ten criteria for birth-death processes presented in Table 1.4 （p. 15） of Prof. Mu-Fa Chen＇s book ＂Eigenvalues, Inequalities and Ergodic
基金supported by Science Fund for Creative Research Groups of National Natural Science Foundation of China (No.10121101)National Basic Research Program of China(Grant No.2006CB805901)
文摘By establishing the intrinsic super-Poincar'e inequality,some explicit conditions are presented for diffusion semigroups on a non-compact complete Riemannian manifold to be intrinsically ultracontractive.These conditions,as well as the resulting uniform upper bounds on the intrinsic heat kernels,are sharp for some concrete examples.
基金Supported by ANR(Grant No.EFI ANR-17-CE40-0030)。
文摘Poincaréinequality has been studied by Bobkov for radial measures,but few are known about the logarithmic Sobolev inequality in the radial case.We try to fill this gap here using different methods:Bobkov's argument and super-Poincaréinequalities,direct approach via L_(1)-logarithmic Sobolev inequalities.We also give various examples where the obtained bounds are quite sharp.Recent bounds obtained by Lee–Vempala in the log-concave bounded case are refined for radial measures.
