Regularity of the inverse mapping in Banach function spaces

Anastasia Molchanova; Tomáš Roskovec; Filip Soudský

Regularity of the inverse mapping in Banach function spaces

Functional Analysis 2021-01-13 v2

Authors: Anastasia Molchanova , Tomáš Roskovec , Filip Soudský

Abstract

We study the regularity properties of the inverse of a bilipschitz mapping $f$ belonging $W^m X_{\text{loc}}$ , where $X$ is an arbitrary Banach function space. Namely, we prove that the inverse mapping $f^{-1}$ is also in $W^m X_{\text{loc}}$ . Furthermore, the paper shows that the class of bilipschitz mappings in $W^m X_{\text{loc}}$ is closed with respect to composition and multiplication.

Keywords

banach spaces banach space properties lipschitz spaces

Cite

@article{arxiv.1901.01878,
  title  = {Regularity of the inverse mapping in Banach function spaces},
  author = {Anastasia Molchanova and Tomáš Roskovec and Filip Soudský},
  journal= {arXiv preprint arXiv:1901.01878},
  year   = {2021}
}

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