# Lipschitz and H"older Continuity in Reproducing Kernel Hilbert Spaces

arXiv: https://arxiv.org/abs/2310.18078 · HTML: https://mlsanity.com/paper/2310.18078/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 31 references that are in the map.
- First posted on arXiv 27 Oct 2023.

## Builds on (most cited first, 3 of 3)

- [Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression](https://mlsanity.com/paper/2105.02796/) (2021)
- [D2KE: From Distance to Kernel and Embedding](https://mlsanity.com/paper/1802.04956/) (2018)
- [Learning-enhanced robust controller synthesis with rigorous statistical and control-theoretic guarantees](https://mlsanity.com/paper/2105.03397/) (2021)

## Built on by (most cited first, 3 of 3)

- [On Safety in Safe Bayesian Optimization](https://mlsanity.com/paper/2403.12948/) (2024)
- [Explainable Binary Classification of Separable Shape Ensembles](https://mlsanity.com/paper/2410.12994/) (2024)
- [Safe and Near-Optimal Control with Online Dynamics Learning](https://mlsanity.com/paper/2509.16650/) (2025)

## Abstract (arXiv)

Reproducing kernel Hilbert spaces (RKHSs) are very important function spaces, playing an important role in machine learning, statistics, numerical analysis and pure mathematics. Since Lipschitz and H"older continuity are important regularity properties, with many applications in interpolation, approximation and optimization problems, in this work we investigate these continuity notion in RKHSs. We provide several sufficient conditions as well as an in depth investigation of reproducing kernels inducing prescribed Lipschitz or H"older continuity. Apart from new results, we also collect related known results from the literature, making the present work also a convenient reference on this topic.