This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary c...This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincare and the logarithmic Sobolev inequalities in the present context.展开更多
Some estimates of logarithmic Sobolev constant for general symmetric forms are obtained in terms of new Cheeger’s constants. The estimates can be sharp in some sense.
Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the ext...Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the extended stochastic integrals is obtained.展开更多
基金Research supported in part by NSFC (No. 19631060), Math. Tian Yuan Found., Qiu Shi Sci. & Tech. Found., RFDP and MCME
文摘This paper deals with the Nash inequalities and the related ones for general symmetric forms which can be very much unbounded. Some sufficient conditions in terms of the isoperimetric inequalities and some necessary conditions for the inequalities are presented. The resulting conditions can be sharp qualitatively as illustrated by some examples. It turns out that for a probability measure, the Nash inequalities are much stronger than the Poincare and the logarithmic Sobolev inequalities in the present context.
文摘Some estimates of logarithmic Sobolev constant for general symmetric forms are obtained in terms of new Cheeger’s constants. The estimates can be sharp in some sense.
基金supported by National Natural Science Foundation of China (Grant No.10961012)Natural Sciences and Engineering Research Council of Canada (Grant No. 311945-2008)
文摘Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the extended stochastic integrals is obtained.
