正定自伴算子分数幂的泛函不等式  

FUNCTIONAL INEQUALITIES FOR FRACTIONAL POWERS OF POSITIVE DEFINITE SELF-ADJOINT OPERATORS

作　　者：刘伟[1] 孙国正[1] 

机构地区：[1]安徽师范大学数学计算机科学学院,安徽芜湖241000

出　　处：《数学杂志》2007年第2期233-236,共4页Journal of Mathematics

基　　金：安徽省教育厅自然科学研究项目(2003KJ165)

摘　　要：本文研究了super-Poincaré不等式在变换下的稳定性.利用自伴算子的谱分解性质,证明了当正定自伴算子L满足super-Poincaré不等式时,L的分数幂Lα也满足相应的super-Poincaré不等式,并讨论了相应半群的几种超有界性之间的关系.The stability of super-Poincaré inequality under transformation is studied in this paper by using the spectral decomposation of self-adjoint operator. Assuming that a super-Poincaré inequality is satisfied by a positive definite self-adjoint operator L, we prove the corresponding inequality for the fractional powers of L. We also discuss the hyperbounded, superbounded and ultrabounded properties for the corresponding semigroups.

关 键 词：super-Poincaré不等式 算子的分数幂 超有界性 

分 类 号：O177.2[理学—数学]