- E19
[10M] Let be given \(p,q∈[1,∞]\) such that \(1/p + 1/q = 1\) 1 and \(x,y∈ℝ^ n\); show the Hölder inequality in this form
\begin{equation} ∑_{i=1}^ n|x_ i y_ i| ≤ \| x\| _ p \| y\| _ q\quad .\label{eq:dis_ Holder_ val_ ass} \end{equation}20In what cases is there equality?
Tips: Fix \(x_ i,y_ i≥ 0\). For the cases with \(p,q{\lt}∞\) you can:
1
EDB — 10M
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English
Authors:
"Mennucci , Andrea C. G."
.
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- normed vector space
- Young inequality
- Hölder inequality
- Lagrange multiplier
- \( \Vert \cdot \Vert _p\) , in \( ℝ ^n\)
- \( \Vert \cdot \Vert _\infty \) , in \( ℝ ^n\)
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