Hardy Type Identities on ℝn−k×(ℝ+)k via Factorizations

Abstract

We establish Hardy type identities on conical domains Rn−k×(R+)k. Our equalities imply several versions of the Hardy type inequalities with exact remainder terms on Rn−k×(R+)k. These equalities provide straightforward understandings of the sharp constants as well as the nonexistence of nontrivial optimizers for various Hardy type inequalities on Rn−k×(R+)k.