Goldstein, Jerome A.Kömbe, İsmailYener, Abdullah2020-11-212020-11-2120180026-9255https://doi.org/10.1007/s00605-017-1060-zhttps://hdl.handle.net/11467/3517We give a simple sufficient criterion on a pair of nonnegative weight functions a and b on a Carnot group G, so that the following general weighted Lp Rellich type inequality?Ga|?Gu|pdx??Gb|u|pdxholds for every u?C0?(G) and p> 1. It is worthwhile to notice that our method easily derives previously known weighted Rellich type inequalities with a sharp constant in a more adequate fashion and also enables us to obtain new ones. We also present a sharp Lp Rellich type inequality that connects first to second order derivatives and some new two-weight Rellich type inequalities with remainders on bounded domains ? in G via a differential inequality and the improved two-weight Hardy inequality in Goldstein et al. (Discret Contin Dyn Syst 37:2009–2021, 2017). © 2017, Springer-Verlag Wien.eninfo:eu-repo/semantics/closedAccessCarnot groupsRemainder termWeighted Rellich inequalityArticle18614972Q2WOS:000430395800004Q22-s2.0-8501971616410.1007/s00605-017-1060-z