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| rev | Bot | (Created page with "<div class="d-none"><math> \newcommand{\mathds}{\mathbb}</math></div>Prove that for <math>p\in(1,\infty)</math> we have the following Hölder inequality <math display="block"> \left|\frac{x_1+\ldots+x_N}{N}\right|^p\leq\frac{|x_1|^p+\ldots+|x_N|^p}{N} </math> and that for <math>p\in(0,1)</math> we have the following reverse Hölder inequality <math display="block"> \left|\frac{x_1+\ldots+x_N}{N}\right|^p\geq\frac{|x_1|^p+\ldots+|x_N|^p}{N} </math> with in both cases e...") | Apr 20'25 at 1:30 | +529 |