Poincare Inequalities on a Countable Set E and Ω = {x:0 ≤ x_i ≤ a, i =1,2,...,n}

摘要

In the study of Poincar6 inequalities, most of the traditional methods were based on the bounded domain in n dimensional Euclidean space R~n, while the method in this paper is based on a countable set E and accordingly the accurate expressions of Poincare inequalities ‖ (f-μ(f))~n ‖_B ≤ cD (f, f) is presented to expand the research and application scope. As to inequalities for Ω = {x:0 ≤ x_i ≤ a, i =1,2,...,n}, the existing studies was usually made for n=2, but such an inequality was not the best. Therefore, the different values of n is discussed in this paper, and accordingly the accurate expressions of Poincare' inequalities is presented.