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arXiv · 2007.10070

Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity

Martí Prats
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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.

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Martí Prats. 2020-07-20. Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity. https://doi.org/10.1016/j.jat.2023.105985

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