Mathematical Inequalities and Applications, cilt.19, sa.3, ss.937-948, 2016 (SCI-Expanded)
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.