Discrete H\" older and reversed Hardy-type inequalities in Lorentz sequence spaces

We establish new optimal reversed Hardy-type inequalities on the cone of decreasing sequences from ${\mathrm{\ell }}^p$-spaces with power weights, as well as estimates between different norms in Lorentz spaces of sequences. Based on these inequalities, we derive a sharp Hölder-type inequality in Lorentz sequence spaces that complements the previously considered case of functions.