Abstract
In the present paper we prove several sharp two-weight Hardy, Hardy-Poincaŕe, and Rellich type inequalities on the sub-Riemannian manifold R2n+1 = Rn x Rn xR defined by the vector fields: Xj = ∂ /∂ xj +2kyj |z|2k?2 ∂/ ∂ l Yj = ∂ /∂ yj ?2kxj |z|2k?2∂/ ∂ l, j = 1,2, ..,n where (z,y) = (x,y, l) ∂ R2n+1 , |z| = (|x|2 +|y|2)1/2 and k ≥ 1.
Original language | English |
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Pages (from-to) | 937-948 |
Number of pages | 12 |
Journal | Mathematical Inequalities and Applications |
Volume | 19 |
Issue number | 3 |
DOIs | |
Publication status | Published - Jul 2016 |
Keywords
- Hardy inequality with two weight functions
- Rellich inequality with two weight functions
- Sharp constan