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Hardy and Rellich inequalities with exact missing terms on homogeneous groups

Authors: 

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

Source title: 
Journal of the Mathematical Society of Japan, 71(4): 1243-1256, 2019 (ISI)
Academic year of acceptance: 
2019-2020
Abstract: 

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.