摘要
从一个给定Dirichlet型的泛函不等式出发,得到了分式次Dirichlet型的相应泛函不等式。作为应用,建立了分数次Dirichlet型的若干具体不等式,包括超Poincaré不等式,弱Poincaré不等式,和本质超Poincaré不等式,一些典型例子表明,我们的结果是精确的。
Based on the functional inequality for a given Dirichlet form,the same type inequality is established for the quadric form associated to the generator with a power.As applications,some concrete functional inequalities, including the super Poincaréinequality,the weak Poincare inequality,and the intrinsic super Poincaréinequality, are studied for Dirichlet operators with powers.Some simple examples are provided to show the optimality of the main result.
基金
国家创新群体研究基金(10121101)
博士点基金(20040027009)
973计划资助项目
