General weighted hardy type inequalities related to Baouendi-Grushin operators

KÖMBE İ., YENER A.

Complex Variables and Elliptic Equations, vol.63, no.3, pp.420-436, 2018 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 63 Issue: 3
  • Publication Date: 2018
  • Doi Number: 10.1080/17476933.2017.1318128
  • Journal Name: Complex Variables and Elliptic Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.420-436
  • Keywords: Baouendi-Grushin vector fields, weighted Hardy inequality, Heisenberg-Pauli-Weyl inequality, two-weight Hardy inequality, remainder terms
  • İstanbul Ticaret University Affiliated: Yes

Abstract

In this paper, we derive a sufficient condition on a pair of nonnegative weight functions ϑ and w in ℝm+k so that the general weighted Hardy type inequality with a remainder term (Formula Presented) is the sub-elliptic gradient. It is worth emphasizing here that our unifying method may be readily used to recover most of the previously known sharp weighted Hardy and Heisenberg-Pauli-Weyl type inequalities as well as to construct other new inequalities with an explicit constant. Furthermore, we also obtain new results on two-weight Lp Hardy type inequalities with remainder terms on smooth bounded domains Ω in ℝm+k via a non-linear partial differential inequality.