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

In this paper, we give an extension of the classical Caffarelli-Kohn-Nirenberg inequalities with respect to the range of parameters. We also establish best constants for large families of parameters. Moreover, we also obtain anisotropic versions of these inequalities which can be conveniently formulated in the language of Folland and Stein's homogeneous groups. We also establish sharp Hardy type inequalities in L-p, 1 < p < infinity, with super-weights