= History of Hölder's inequality
<Otto Hölder>'s 1889 paper begins with a weighted-mean inequality for a <function> with increasing <derivative>. In current terminology, its opening statement is a weighted form of <Jensen's inequality>: applying a <convex function> after taking a <weighted mean> gives a lower bound for the weighted mean of its values. This connects product estimates to the geometry of <convex functions>, rather than treating them as isolated formulas.<Ueber einen Mittelwerthssatz by Otto Hölder>[Otto Hölder, Ueber einen Mittelwerthssatz (1889), §§1–2, printed pp. 38–39: weighted means and increasing derivative]{ref}
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