Kömbe, İsmailYener, Abdullah2020-11-212020-11-2120181747-6933https://doi.org/10.1080/17476933.2017.1318128https://hdl.handle.net/11467/3786In this paper, we derive a sufficient condition on a pair of nonnegative weight functions ? and w in ?m+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 ? in ?m+k via a non-linear partial differential inequality. © 2017 Informa UK Limited, trading as Taylor & Francis Group.eninfo:eu-repo/semantics/closedAccessBaouendi-Grushin vector fieldsHeisenberg-Pauli-Weyl inequalityRemainder termsTwo-weight Hardy inequalityWeighted Hardy inequalityArticle633420436Q2WOS:000426903500009Q22-s2.0-8501972364910.1080/17476933.2017.1318128