A general approach to weighted $L^{p}$ Rellich type inequalities related to Greiner operator

Abstract

In 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 ϑ of the Greiner operator ∆ k such that