TY - JOUR
T1 - Hardy and rellich type inequalities with two weight functions
AU - Ahmetolan, Semra
AU - Kombe, Ismail
PY - 2016/7
Y1 - 2016/7
N2 - 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.
AB - 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.
KW - Hardy inequality with two weight functions
KW - Rellich inequality with two weight functions
KW - Sharp constan
UR - http://www.scopus.com/inward/record.url?scp=84989918461&partnerID=8YFLogxK
U2 - 10.7153/mia-19-68
DO - 10.7153/mia-19-68
M3 - Article
AN - SCOPUS:84989918461
SN - 1331-4343
VL - 19
SP - 937
EP - 948
JO - Mathematical Inequalities and Applications
JF - Mathematical Inequalities and Applications
IS - 3
ER -