Orazbayev, Almat2024-06-072024-06-072024-04-29Orazbayev, A. (2024). Improved Hardy-Sobolev inequalities. Nazarbayev University School of Sciences and Humanitieshttp://nur.nu.edu.kz/handle/123456789/7785In this thesis work, a new version of the Hardy-Sobolev inequality is obtained. It covers the recent inequality of Frank, Laptev, and Weidl derived in [4] and improves the results of Persson and Samko established in [13]. It gives new results in one dimension. We analyse radial and non-radial versions of the considered multidimensional Hardy-Sobolev inequality and as a consequence we establish some Heisenberg-Pauli-Weyl uncertainty principles.enAttribution-NonCommercial-NoDerivs 3.0 United StatesType of access: RestrictedHardy-Sobolev inequalitySharp ConstantSymmetric rearrangementsUncertainty principleMaster's thesis