Holder inequality

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Holder's inequality states

LaTeX:  \|x y\|_1 \le \|x\|_p \|y\|_q ,

where LaTeX: \|\cdot\|_k denotes the LaTeX: L_k norm, LaTeX: p > 1, and LaTeX: 1/p + 1/q = 1. Equality holds if and only if LaTeX: |x|^p = a|y|^q for some scalar LaTeX: a. (Note: this is the Cauchy-Schwartz inequality if LaTeX: p = q = 2.)


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