query: $L^p([0,1])$ stricly convex
positive_passages.docid: 149536
positive_passages.text: Why is the  $L_p$ norm strictly convex for $1<p<\infty?$
negative_passages.docid: 150727
negative_passages.text: Characterization convex function.
negative_passages.docid: 89555
negative_passages.text: Inequality for the p norm of a convolution
negative_passages.docid: 32092
negative_passages.text: Gelfand transformation of $l^p$
negative_passages.docid: 46746
negative_passages.text: How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
negative_passages.docid: 26658
negative_passages.text: A proof for $\nabla |u|^p = p\ \text{sgn}(u)|u|^{p-1}\nabla u$.
negative_passages.docid: 74608
negative_passages.text: Convex function as supremum of countably many affine functions
negative_passages.docid: 87207
negative_passages.text: Prove that the support function of an arbitrary set $A\subset\mathbb R^n$ is convex
negative_passages.docid: 40403
negative_passages.text: Show that the function is convex
negative_passages.docid: 16463
negative_passages.text: Is the function $\mbox{tr}(XAX')$ convex?
negative_passages.docid: 115495
negative_passages.text: Prove $\int _0^\infty f^2 dx \leq \cdots $ for $f$ convex
negative_passages.docid: 51267
negative_passages.text: Showing a generalized version of the Hölder inequality for $L^{p}$ spaces
negative_passages.docid: 102079
negative_passages.text: If $1\leq p < \infty$ then show that $L^p([0,1])$ and $\ell_p$ are not topologically isomorphic
negative_passages.docid: 124844
negative_passages.text: Show that $\phi \circ f$ belongs to $L_p$ for each $f \in L_p$
negative_passages.docid: 92029
negative_passages.text: Is this rational function convex?
negative_passages.docid: 67313
negative_passages.text: Proving $\{(x_1, x_2) \in \mathbb{R}^2_{+} \mid x_1 x_2 \geq 1\}$ is convex
negative_passages.docid: 63516
negative_passages.text: $C^1[0,1]$ is not complete with respect to sup norm