Suppose \(\mathbb{K}\) is either \(\mathbb{R}\) or \(\mathbb{C}\) and \(p\in (0,\infty)\). The \(l^p\)-norm of a vector \(x\in \mathbb{K}^d\) is given by

\[ \lVert x\rVert_{p,\infty }=\sup_{t>0}\lvert \{j\in {1,\ldots ,d} \mid \lvert x_j\rvert\ge t\}\rvert^{1/p}\cdot t. \]

[1]

See also Link to heading

• connection to non-increasing rearrangement of \(x\)
• comparison with \(l^p\)-norm

References Link to heading

1. I. Veselic. Class Lecture, Topic: Compressive Sensing. Technische Universität Dortmund, 2017.