A unified approach to weighted Hardy type inequalities on Carnot groups

Goldstein J. A., KÖMBE İ., YENER A.

Discrete and Continuous Dynamical Systems- Series A, vol.37, no.4, pp.2009-2021, 2017 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 4
  • Publication Date: 2017
  • Doi Number: 10.3934/dcds.2017085
  • Journal Name: Discrete and Continuous Dynamical Systems- Series A
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2009-2021
  • Keywords: Carnot groups, weighted Hardy inequality, Heisenberg-Pauli-Weyl inequality, two-weight Hardy inequality
  • İstanbul Ticaret University Affiliated: Yes

Abstract

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.