Seitkan M.2025-06-132025-06-132023Seitkan M / Hypoelliptic functional inequalities and applications / 7M05401 - Department of Mathematics and Natural Sciences / 2023https://repository.sdu.edu.kz/handle/123456789/1760In this thesis we discuss cylindrical extensions of the improved Rellich inequalities on R* x R"-* with the Euclidean norm |- |, on R*. Actually, we show sharp remainders of the Rellich type inequalities yielding the classical Rellich inequality. Moreover, Rellich type identities and inequalities with more general weights are established. In addition, we present horizontal extensions of these results on stratified Lie groups.enRellich inequalityLie groupsPreliminariesThesis