Hardy and Rellich inequalities with exact missing terms on homogeneous groups

Duy Tuan Nguyen; Nguyen Lam-Hoang; Triet Anh Nguyen

doi:10.2969/jmsj/80878087

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Hardy and Rellich inequalities with exact missing terms on homogeneous groups

Duy Tuan Nguyen, Nguyen Lam-Hoang, Triet Anh Nguyen

著者情報

キーワード: Hardy inequality, Hardy–Rellich inequality, Bessel pair, remainder term, homogeneous Lie group

ジャーナルフリー

2019 年 71 巻 4 号 p. 1243-1256

DOI https://doi.org/10.2969/jmsj/80878087

詳細

抄録

We prove several identities on homogeneous groups that imply the Hardy and Rellich inequalities for Bessel pairs. These equalities give a straightforward understanding of some of the Hardy and Rellich inequalities as well as the absence of nontrivial optimizers and the existence/nonexistence of “virtual”extremizers.