Ruzhansky, MichaelSuragan, Durvudkhan2019-12-132019-12-132019Ruzhansky, M., Suragan, D. (2019). CRITICAL HARDY INEQUALITIEShttps://doi.org/10.5186/aasfm.2019.4467http://nur.nu.edu.kz/handle/123456789/4452We prove a range of critical Hardy inequalities and uncertainty type principles on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. Moreover, we establish a new type of critical Hardy inequality and prove Hardy-Sobolev type inequalities. Most of the obtained estimates are new already for the case of R-n. For example, for any f is an element of C-0(infinity) (R-n \ { 0 }) we obtain the range of critical Hardy inequalities of the formenAttribution-NonCommercial-ShareAlike 3.0 United StatesArticle