Kömbe, İsmailYener, Abdullah2020-11-212020-11-2120170002-9939https://doi.org/10.1090/proc/13730https://hdl.handle.net/11467/3494We find a simple sufficient criterion on a pair of nonnegative weight functions a (x, y) and b (x, y) in ?m+k so that the general weighted Lp Rellich type inequality (Formula presented) holds for all u ? C0?(?m+k). Here ?? = ?x + |x|2??y is the Baouendi-Grushin operator, ? > 0, m, k ? 1 and p > 1. It is important to point out here that our approach is constructive in the sense that it allows us to retrieve already established weighted sharp Rellich type inequalities as well as to get other new results with an explicit constant on ?m+k. We also obtain a sharp Lp Rellich type inequality that connects first to second order derivatives and several new two-weight Rellich type inequalities with remainder terms on smooth bounded domains ? in ?m+k via a nonlinear differential inequality. © 2017 American Mathematical Society.eninfo:eu-repo/semantics/closedAccessBaouendi-Grushin vector fieldsRemainder termTwo-weight Rellich inequalityWeighted Rellich inequalityArticle1451148454857Q2WOS:000409193700024Q12-s2.0-8502958183510.1090/proc/13730