Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity
Classical Analysis and ODEs
2024-02-12 v4
Abstract
We study the stability of Triebel-Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse function of a Triebel-Lizorkin bi-Lipschitz map in Lipschitz domains. To obtain the results we provide an equivalent norm for the Triebel-Lizorkin spaces with fractional smoothness in uniform domains in terms of the first-order difference of the last weak derivative available averaged on balls.
Cite
@article{arxiv.2007.10070,
title = {Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity},
author = {Martí Prats},
journal= {arXiv preprint arXiv:2007.10070},
year = {2024}
}
Comments
6 figures, funding information added. To appear in Journal of Approximation Theory