By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery＇s argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As appli...By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery＇s argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems. In particular, some results in [1, 2] are generalized.展开更多
基金Project supported by the National Natural Scienoe Fbundation of China (No.10121101)the Research Fund for the Doctoral Program of Higher Education (No.20040027009).
文摘By using the dimension-free Harnack inequality, the coupling method, and Bakry-Emery＇s argument, some explicit lower bounds are presented for the constant of the Beckner type inequality on compact manifolds. As applications, the Beckner inequality and the transportation cost inequality are established for a class of continuous spin systems. In particular, some results in [1, 2] are generalized.
