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Deducing properties of the $\ell_3$ norm from the $\ell_1$ and $\ell_2$ norms
Suppose we have a function $f: [0,1] \rightarrow \mathbb{R}$, $f(x) \geq 0$ normalised so that $\|f\|_1 = 1$, where
$$
\| f\|_p = \left( \int_0^1 f(x)^p d x \right)^{1/p}.
$$
Moreover, we know that $\|...
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Norm equivalence constants
Take a polynomial $g\in\mathbb{R}[\mathbf{x}]$, in $n$ variables and having some degree $d$, with $g(\mathbf{x})\geq 0$. We define the $p$-norms of $g$ as
$$
\vert \vert g \vert \vert _{p} = \left( \...
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