Weighted Hardy-type inequalities

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dc.contributor.authorAtina A.
dc.date.accessioned2026-09-08T10:22:59Z
dc.date.available2026-09-08T10:22:59Z
dc.date.issued2026
dc.description.abstractThis thesis is devoted to weighted Hardy-type inequalities and identities obtained by the factorization method. The main focus is on Hardy-type identities in the Baouendi–Grushin setting, where the Euclidean radial derivative is replaced by the radial derivative associated with the Grushin structure. More precisely, we consider the homogeneous distance function ρ and the Grushin gradient ∇γ, and study identities involving the radial Grushin derivative ∇γρ · ∇γu |∇γρ| . Using suitable first-order differential operators and their formal adjoints, we derive an improved weighted Hardy identity with an explicit non-negative remainder term. The result is formulated under the assumption that the weight functions V and W form a Bessel pair adapted to the homogeneous dimension Q. The obtained identity extends classical radial Hardy-type identities with Bessel pairs to the degenerate Baouendi–Grushin framework. Several special cases are also discussed, including power-type and logarithmic weights, which illustrate how the general theorem leads to concrete weighted Hardy-type inequalities.
dc.identifier.citationAtina A / Weighted Hardy-type inequalities / SDU University / Department of Mathematics and Natural Sciences
dc.identifier.urihttps://repository.sdu.edu.kz/handle/123456789/2652
dc.language.isoen
dc.publisherSDU University
dc.subjectHardy identity
dc.subjectapplications and special cases
dc.subjectBessel pairs
dc.titleWeighted Hardy-type inequalities
dc.typeThesis

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