Three weights higher order Hardy type inequalities

We investigate the following three weights higher order Hardy type inequality (0.1) ‖g‖q,u≤  C‖Dρkg‖p,v where Dρi denotes the following weighted differential operator: {dig(t)dti,i=0,1,...,m−1,di−mdti−m(p(t)dmg(t)dtm),i=m,m+1,...,k, for a weight function ρ(⋅). A complete description of the weights u, v and ρ so that (0.1) holds was given in [4] for the case 1

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