Some Hardy identities on half‐spaces

We prove some Hardy identities on the half‐space R+N$\mathbb {R}_{+}^{N}$. Our equalities imply correponding versions of the Hardy type inequalities with exact remainder terms on R+N$\mathbb {R}_{+}^{N}$. These equalities give straightforward understandings of the optimal constants as well as the no...

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Bibliographic Details
Published inMathematische Nachrichten Vol. 294; no. 12; pp. 2317 - 2328
Main Authors Duy, Nguyen Tuan, Lam, Nguyen, Phi, Le Long
Format Journal Article
LanguageEnglish
Published Weinheim Wiley Subscription Services, Inc 01.12.2021
Subjects
Bessel pair
Hardy inequality
Inequalities
sharp constant
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Summary:We prove some Hardy identities on the half‐space R+N$\mathbb {R}_{+}^{N}$. Our equalities imply correponding versions of the Hardy type inequalities with exact remainder terms on R+N$\mathbb {R}_{+}^{N}$. These equalities give straightforward understandings of the optimal constants as well as the nonexistence of nontrivial optimizers for various Hardy type inequalities on half‐spaces. These identities also provide the “virtual” ground state in the sense of Frank and Seiringer [13] for several Hardy type inequalities on R+N$\mathbb {R}_{+}^{N}$.
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.201900312