English

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}
}