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Öğe Hardy and rellich type inequalities with two weight functions(Element D.O.O., 2016) Ahmetolan, Semra; Kömbe, İsmailIn the present paper we prove several sharp two-weight Hardy, Hardy-Poinca?e, 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.Öğe Improved hardy and rellich type inequalities with two weight functions(Element D.O.O., 2018) Ahmetolan, Semra; Kömbe, İsmailIn this work, we obtain several improved versions of two weight Hardy and Rellich type inequalities on the sub-Riemannian manifold R 2 n+ 1 defined by the vector fields ? ? X j = ? x j + 2ky j |z| 2 k? 2 ? ? l , Y j = ? y j ? 2kx j |z| 2 k? 2 ? ? l , j = 1, 2,..., n where (z, l) = (x, y, l) ? R 2 n+ 1 , |z| = (|x| 2 + |y| 2 ) 1 / 2 and k 1 . © 2018 Element D.O.O. All rights reserved.Öğe A sharp uncertainty principle and hardy-poinca?e inequalities on sub-riemannian manifolds(Element D.O.O., 2012) Ahmetolan, Semra; Kömbe, İsmailWe prove a sharp Heisenberg uncertainty principle inequality and Hardy-Poinca?e inequality on the sub-Riemannian manifold R2n+1 = Rn ×Rn ×R defined by the vector fields: where |z| = (|x|2 +|y|2)1/2 and k1.
