Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity
arXiv:2007.10070 · doi:10.1016/j.jat.2023.105985
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.
6 figures, funding information added. To appear in Journal of Approximation Theory
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