Gagliardo-Nirenberg inequality with H\"older norms
Functional Analysis
2025-05-27 v2
Abstract
The classical Gagliardo-Nirenberg inequality, known as an interpolation inequality, involves Lebesgue norms of functions and their derivatives. We established an interpolation lemma to connect Lebesgue and H\"older spaces, thus extending the Gagliardo-Nirenberg inequality. This extension involved substituting arbitrary Sobolev norms with appropriate H\"older norms, allowing for a wider range of applicable parameters in the inequality.
Keywords
Cite
@article{arxiv.2405.00941,
title = {Gagliardo-Nirenberg inequality with H\"older norms},
author = {Mengxia Dong},
journal= {arXiv preprint arXiv:2405.00941},
year = {2025}
}