# A generalization of Young's $L^p$ inequality

Borwein, Jonathan M. (1997) A generalization of Young's $L^p$ inequality. Mathematical Inequalities and Applications, 1 . pp. 131-136.

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Postscript
We show that, for positive real numbers with $a \ge 1+ \sum_i^N \alpha_i$, the function $${r^a \over{a}} \over{ \prod_{i=1}^N x_i^{\alpha_i}}$$ has a convex conjugate of the same form and so, in particular, obtain a clean proof that $f$ is convex.
Item Type: Article pubdom FALSE Fenchel conjugate, Young $\ell^p$-inequality, convexity 90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming52-xx Convex and discrete geometry > 52Axx General convexity26-xx Real functions > 26Axx Functions of one variable UNSPECIFIED Users 1 not found. 25 Nov 2003 13 Jan 2015 16:53 https://docserver.carma.newcastle.edu.au/id/eprint/189