Kömbe, İsmailYener, Abdullah2020-11-212020-11-2120191534-0392https://doi.org/10.3934/cpaa.2019042https://hdl.handle.net/11467/3765In this paper we exhibit some sufficient conditions that imply general weighted L p Rellich type inequality related to Greiner operator without assuming a priori symmetric hypotheses on the weights. More precisely, we prove that given two nonnegative functions a and b, if there exists a positive supersolution ? of the Greiner operator ? ? such that ? ? (a|? ? ?| p-2 ? ? ?)?b? p-1 almost everywhere in R 2n+1 ; then a and b satisfy a weighted L p Rellich type inequality. Here, p > 1 and ? ? = ? n j=1 (x 2 j +y 2 j ) is the sub-elliptic operator generated by the Greiner vector fields x j {equation presented} where (z,l)=(x,y,l)? R 2n+1 =R n ×R n ×R,|Z|={equation presented} and k ? 1. The method we use is quite practical and constructive to obtain both known and new weighted Rellich type inequalities. On the other hand, we also establish a sharp weighted L p Rellich type inequality that connects first to second order derivatives and several improved versions of two-weight L p Rellich type inequalities associated to the Greiner operator ? ? on smooth bounded domains ? in R 2n+1 . © 2019 American Institute of Mathematical Sciences. All Rights Reserved.eninfo:eu-repo/semantics/closedAccessGreiner operatorRemainder termWeighted Rellich inequalityArticle182869886Q2WOS:000446873800015Q12-s2.0-8505495242310.3934/cpaa.2019042