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VOL. 81 | 2019 Remarks on the Hardy type inequalities with remainder terms in the framework of equalities
Shuji Machihara, Tohru Ozawa, Hidemitsu Wadade

Editor(s) Keiichi Kato, Takayoshi Ogawa, Tohru Ozawa

Abstract

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.

Information

Published: 1 January 2019
First available in Project Euclid: 31 October 2019

zbMATH: 07176823

Digital Object Identifier: 10.2969/aspm/08110247

Subjects:
Primary: 26D10, 46E35

Rights: Copyright © 2019 Mathematical Society of Japan

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