Extended Caffarelli–Kohn–Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities

Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups

“…[Gri03,AS06,DD14,KÖ13]. Refinements including boundary terms over arbitrary domains have been obtained by the authors in [RS17] (see also [RS17a], [RS17b] and [RSY17]), and further local weighted versions for sums of squares of vector fields of possibly limited regularity on manifolds were recently established in [RS17c].…”

Fractional logarithmic inequalities and blow-up results with logarithmic nonlinearity on homogeneous groups

“…Recently many different versions of Caffarelli-Kohn-Nirenberg inequalities have been obtained on different Lie groups, namely, in [26] on the Heisenberg groups, in [22] and [23] on stratified groups, in [19] and [21] on (general) homogeneous groups. On the homogeneous groups a fractional analogue of Caffarelli-Kohn-Nirenberg inequality was proved in [14].…”

Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups

“…For examples, the CKN inequalities was generalized to the stratified Lie groups, the homogeneous groups, the metric measure spaces, to Riemannian manifolds with negative curvature and to derivatives of fractional order, etc. We refer the readers to [5,7,8,6,13,15,16,17,18,20,21,24,23,25] for dicussions on this subject. It is an interesting and non-trivial problem to look for the sharp constant in the CKN inequalities (1.4).…”