Some Remarks Concerning the Hardy Inequality

Abstract

This note deals with the Hardy inequality of order k

$${(\int_0^\infty {|u(t)} {|^q}{w_0}(t)dt)^{1/q}} \leqslant C{(\int_0^\infty {|{u^{(k)}}} (t){|^p}{w_k}(t)dt)^{1/p}},$$

(1)

more precisely, with conditions on the parameters p,q and on the weight functions w ₀, w _k under which inequality (1) holds for all functions u from a certain class K with a constant C > 0 independent of u.