Resumen de Higher order Hardy inequalities

Alois Kufner

• This note deals with the inequality $$\bigg(\int^b_a\vert u(x)\vert^qw_0(x)dx\bigg)^{1/q}\leq C\bigg(\int^b_a \vert u^{(k)}(x)\vert^pw_k(x)dx\bigg)^{1/p} ,\qquad (1)$$ more precisely, with conditions on the parameters $p > 1, q > 0$ and on the weight functions $w_0, w_k$ (measurable and positive almost everywhere) which ensure that (1) holds for all functions $u$ from a certain class $K$ with a constant $C > 0$ independent of $u$.