Hardy–Littlewood–Sobolev and Stein–Weiss inequalities on homogeneous Lie groups - Aidyn Kassymov; Michael Ruzhansky; Durvudkhan Suragan (My University, 2019)
In this note, we prove the Stein–Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy–Littlewood–Sobolev inequality on general homogeneous Lie groups.
Keywords: Riesz potential; Hardy–Littlewood–Sobolev inequality; Stein–Weiss inequality; fractional operator; fractional integral; homogeneous Lie group