Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for L^p-weighted Hardy inequalities · arXivDesk
1701.01280Jan 5, 201731 pages; new inequalities have been added yielding also new results on Rn, namely, extended Caffarelli-Kohn-Nirenberg inequalities and $L^{p}$-weighted Hardy inequalities with superweights. Therefore, the title has been also changed
Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for Lp-weighted Hardy inequalities
Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov
Moreover, we also obtain anisotropic versions of these inequalities which can be conveniently formulated in the language of Folland and Stein's homogeneous groups. Consequently, we obtain remainder estimates for
Lp
-weighted Hardy inequalities on homogeneous groups, which are also new in the Euclidean setting of
Rn
. The critical Hardy inequalities of logarithmic type and uncertainty type principles on homogeneous groups are obtained. Moreover, we investigate another improved version of
Lp
-weighted Hardy inequalities involving a distance and stability estimates. We also establish sharp Hardy type inequalities in
Lp
,
1<p<∞
, with superweights, i.e. with the weights of the form