超Poincaré不等式在L^p空间上的推广及应用  

Generalization and Application of Super-Poincare Inequality on L^p-space

作　　者：刘伟[1] 孙国正[2] 

机构地区：[1]北京师范大学数学科学学院,北京100875 [2]安徽师范大学数学计算机科学学院,芜湖241000

出　　处：《数学物理学报（A辑）》2007年第5期781-787,共7页Acta Mathematica Scientia

基　　金：国家自然科学基金创新群体研究基金(NSFC10121101);安徽省教育厅自然科学研究基金(2003KJ165)资助

摘　　要：该文建立了Lp(μ)空间上的超Poincare不等式,得到了Lp(μ)上半群的半紧性和紧性的充要条件及相应的扰动结果,同时给出超Poincare不等式成立的一个充分条件,推广了L2(μ)上的相关结论.作为应用,文中最后讨论了黎曼流形上一类非对称扩散算子的本质谱.　The authors establish the super-Poincare inequality on L^p-space with respect to a measure space, and obtain some necessary and sufficient conditions about semicompact and compact property of semigroup and the perturbation result. Meanwhile, a sufficient condition for super-Poincare inequality is shown, which generalizes some known results obtained on the L^2-space. As applications, the essential spectrum of a class of non-symmetric diffusion operators on Riemannian manifold is studied.

关 键 词：超Poincare不等式 紧半群 渐近核 扰动 本质谱 

分 类 号：O177.2[理学—数学]