Why Hölder's inequality should be called Rogers' inequality

This reviewer remembers Leopold Fejér (1880-1959) saying (in Hungarian) that ``the history of mathematics serves to prove that nobody discovered anything: there was always somebody who had known it before'' (quoted in English in the present paper). The author argues convincingly about who had priority to the inequalities of Hölder (Rogers), Cauchy (Lagrange), Jensen (Hölder) and others. Also equivalences and relations between different forms and different inequalities and several proofs are offered. The paper concludes with biographical sketches of Leonard James Rogers and Otto Ludwig Hölder.