Abstract
Motivated by the work of Ghoussoub and Moradifam, we prove some improved Hardy inequalities on the Heisenberg group ℍ n via Bessel function. Mathematics Subject Classification (2000): Primary 26D10
Highlights
Hardy inequality in RN reads, for all u ∈ C∞ 0 (RN) and N ≥ 3,|∇u|2dx ≥ (N − 2)2 4u2 |x|2 dx RN (1:1)and (N − 2)2 is the best constant in (1.1) and is never achieved
Motivated by the work of Ghoussoub and Moradifam, we prove some improved Hardy inequalities on the Heisenberg group Hn via Bessel function
A similar inequality 4 with the same best constant holds in RN is replaced by an arbitrary domain Ω ⊂ RN
Summary
Hardy inequality in RN reads, for all u ∈ C∞ 0 (RN) and N ≥ 3,|∇u|2dx ≥ (N − 2)2 4u2 |x|2 dx RN (1:1)and (N − 2)2 is the best constant in (1.1) and is never achieved. Motivated by the work of Ghoussoub and Moradifam, we prove some improved Hardy inequalities on the Heisenberg group Hn via Bessel function. A similar inequality 4 with the same best constant holds in RN is replaced by an arbitrary domain Ω ⊂ RN Ghoussoub and Moradifam ([4]) give a necessary and sufficient condition on a radially symmetric potential V(|x|) on Ω that makes it an admissible candidate for an improved Hardy inequality.
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