Hardy type identities and inequalities with divergence type operators on smooth metric measure spaces

Abstract

We gave the Hardy type identities and inequalities for the divergence type operator $ L_{f, V} $ on smooth metric measure spaces. Additionally, we improved a Rellich type inequality by using the improved Hardy type inequality. Our results improved and included many previously known results as special cases.

Keywords

• hardy type inequality
• hardy type identity
• smooth metric measure space
• divergence type operator