摘要
本文研究了p-退化椭圆Heisenberg-Greiner算子的一类Hardy不等式的证明问题.利用正则化及逼近的方法,获得了该算子的一类强Hardy不等式的结果,推广了已有文献中p的取值范围,并进一步弥补了去除原点的缺陷.作为应用,讨论了与该算子相关的一类非线性算子的正定性与下无界性,并给出了它的一个正解.
In this paper, we research the problem of the proof to a class of Hardy type inequalities for p-degenerate subelliptic Heisenberg-Greiner operators. By using regularization method and the approximating method to the case here, we get the conclusion of sharp Hardy inequality for the operators. Our results improve the range of p and remedy a defect that eliminate the zero point in the existing results. As applications, we discuss the positive property and the unbounded property from below for p-degenerate subelliptic operator and characterize a positive solution of the nonlinear operator constructed by Heisenberg-Greiner operators.
出处
《数学杂志》
CSCD
北大核心
2011年第4期770-776,共7页
Journal of Mathematics
基金
浙江省自然科学基金资助(Y606144)
