# Smoothness parameter of power of Euclidean norm

arXiv: https://arxiv.org/abs/1907.12346 · HTML: https://mlsanity.com/paper/1907.12346/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2019.

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## Abstract (arXiv)

In this paper, we study derivatives of powers of Euclidean norm. We prove their H"older continuity and establish explicit expressions for the corresponding constants. We show that these constants are optimal for odd derivatives and at most two times suboptimal for the even ones. In the particular case of integer powers, when the H"older continuity transforms into the Lipschitz continuity, we improve this result and obtain the optimal constants.