Improved critical Hardy inequalities on 2-dimensional quasi-balls

In this note we obtain a remainder estimate for improved critical Hardy inequalities on a 2-dimensional quasi-ball on homogeneous Lie groups. These results are new even in the Abelian case of ℝ2 in terms of choosing any choice of homogeneous quasi-norm as well as replacing the full gradient by the radial derivative. © 2017 Author(s).