Improved critical Hardy inequalities on 2-dimensional quasi-balls

2017

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DOI 10.1063/1.5000606
Data confidence 70 medium
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Abstract

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.