Generalizations And Applications Of Functional Inequalities

This thesis is divided into four parts.In the first chapter,the super Poincar inequality is generalized to L~p-space(p is a positive even number)w.r.t a measure space,and a sufficient and necessary condition for compact semi-group and a perturbation result are given,which generalize some known results obtained on the L~2-space w.r.t a measure space.In the second chapter,we study the super-Poincar inequality on L~p-space(1