Levin–Cochran–Lee inequalities and best constants on homogeneous groups

Abstract

In this paper, we apply a direct method instead of a limit approach, for proving the Levin–Cochran–Lee inequalities. First, we state and prove Levin–Cochran–Lee type inequalities on a homogeneous group \(\mathbb {G}\) with parameters \(0<p\le q<\infty \). Furthermore, for the case \(p=q\), we prove the sharp inequalities with power weights and derive some other new inequalities.