0x68072a2a

Suppose \(\mathbb{K}\) is either \(\mathbb{R}\) or \(\mathbb{C}\) and \(p\in (0,\infty)\). For \(x\in \mathbb{K}^N\) the weak \(l^p\)-norm is given by

\[ \lVert x\rVert_{p,\infty }=\max_{1\le k\le N} k^{1/p}x_k^*,\]

where \(x_k^*\) is the \(k\)-th component of the non-increasing rearrangement \(x^*\) of \(x\).