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.