Some Hardy identities on half‐spaces

Abstract

AbstractWe prove some Hardy identities on the half‐space . Our equalities imply correponding versions of the Hardy type inequalities with exact remainder terms on . 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 .