Block mixed norm
= Block mixed norm
{title2=$\|v\|_{q,1}=\sum_i(\sum_r|v_i^r|^q)^{1/q}$}
The block mixed <norm> sums the $\ell^q$ <norm> of each block, for $q\ge1$. Its <dual norm> is $\|p\|_{q',\infty}=\max_i\|p_i\|_{q'}$, where $q'=q/(q-1)$ for $q>1$ and $q'=\infty$ for $q=1$. Apply <Holder inequality> blockwise and choose a norming block to attain equality. <Absolute values> are essential for signed components.