Anisotropic weighted Levin-Cochran-Lee type inequalities on homogeneous Lie groups

Abstract

In this paper, we first prove the weighted Levin-Cochran-Lee type inequalities on homogeneous Lie groups for arbitrary weights, quasi-norms, and $L^p$-and $L^q$-norms. Then, we derive a sharp weighted inequality involving specific weights given in the form of quasi-balls in homogeneous Lie groups. Finally, we also calculate the sharp constants for the aforementioned inequalities.