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On improved fractional Sobolev–Poincaré inequalities

Bartłomiej Dyda Faculty of Pure and Applied Mathematics, Wrocław University of Technology Lizaveta Ihnatsyeva Department of Mathematics, Kansas State University Antti V. Vähäkangas Department of Mathematics and Statistics, University of Jyvaskyla

Analysis of PDEs Functional Analysis mathscidoc:1701.03014

Arkiv for Matematik, 1-18, 2014.5
We study a certain improved fractional Sobolev–Poincaré inequality on domains, which can be considered as a fractional counterpart of the classical Sobolev–Poincaré inequality. We prove the equivalence of the corresponding weak and strong type inequalities; this leads to a simple proof of a strong type inequality on John domains. We also give necessary conditions for the validity of an improved fractional Sobolev–Poincaré inequality, in particular, we show that a domain of finite measure, satisfying this inequality and a ‘separation property’, is a John domain.
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@inproceedings{bartłomiej2014on,
  title={On improved fractional Sobolev–Poincaré inequalities},
  author={Bartłomiej Dyda, Lizaveta Ihnatsyeva, and Antti V. Vähäkangas},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203406715199816},
  booktitle={Arkiv for Matematik},
  pages={1-18},
  year={2014},
}
Bartłomiej Dyda, Lizaveta Ihnatsyeva, and Antti V. Vähäkangas. On improved fractional Sobolev–Poincaré inequalities. 2014. In Arkiv for Matematik. pp.1-18. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203406715199816.
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