Suppose \(\mathbb{K}\) is either \(\mathbb{R}\) or \(\mathbb{C}\) and \(p\in (0,\infty)\). Then for every \(x\in \mathbb{K}^N\) we the following relations hold

1. \(\lVert x\rVert_{p,\infty }\le \lVert x\rVert_p\),
2. \(\lVert x\rVert_p\le (1+\ln N)^{1/p}\lVert x\rVert_{p,\infty }\). [1, Lemma 1.11]

References Link to heading

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