Remarks on the Hardy type inequalities with remainder terms in the framework of equalities
Remarks on the Hardy type inequalities with remainder terms in the framework of equalities
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DOI：
10.2969/aspm/08110247
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
Shuji Machihara;T. Ozawa;H. Wadade
中科院分区：
文献类型：
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作者：
Shuji Machihara;T. Ozawa;H. Wadade
在等式的框架下研究了哈代型不等式.我们提出的等式，立即意味着哈代型不等式下降的剩余项。同时给出了使余项为零的函数类的一个刻划。我们的一个观察点是在一般Hilbert空间中应用一个正交性质，它给出了对哈代型不等式以及非平凡极值的不存在性的一个简单而直接的理解.
We study the Hardy type inequalities in the framework of equalities. We present equalities which immediately imply Hardy type inequalities by dropping the remainder term. Simultaneously we give a characterization of the class of functions which makes the remainder term vanish. A point of our observation is to apply an orthogonality properties in general Hilbert space, and which gives a simple and direct understanding of the Hardy type inequalities as well as the nonexistence of nontrivial extremizers.