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Results tagged with norms
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user 153260
8
votes
A curious norm related to the L¹ norm
I think $C=2$ is the best constant. Consider $\varepsilon>0$ and let $f,g$ continuous in $[0,1]$ defined as follows.
\begin{equation*}
f(x) = \begin{cases} -1, & 0\leq x \leq \frac12 - \varepsilon \\
…
CommunityBot
- 1
4
votes
Accepted
Are these two norms on localized versions of $L^p_q$ equivalent?
The opposite inequality cannot be true. If that were true, then consider a positive function $g$ with the property such that for all $s\in \mathbb{T}$ it holds that $g(s,x) \leq C g(s,y)$ whenever $|x …
