A unified approach to weighted Hardy type inequalities on Carnot groups
We find a simple sufficient criterion on a pair of nonnegative weight functions V (x) and W (x) on a Carnot group G; so that the general weighted Lp Hardy type inequality (Equation presentted) is valid for any φ ∈ C∞0 (G) and p > 1: It is worth noting here that our unifying method may be readily used both to recover most of the previously known weighted Hardy and Heisenberg-Pauli-Weyl type inequalities as well as to construct other new inequalities with an explicit best constant on G: We also present some new results on two-weight Lp Hardy type inequalities with remainder terms on a bounded domain Ω in G via a differential inequality.
Discrete and Continuous Dynamical Systems- Series A
Goldstein, J., Kombe, I., & Yener, A. (2017). A unified approach to weighted Hardy type inequalities on Carnot groups. Discrete and Continuous Dynamical Systems- Series A, 37 (4), 2009-2021. https://doi.org/10.3934/dcds.2017085