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Modulus in Banach function spaces

Vendula Honzlová Exnerová Charles University Jan Malý Charles University Olli Martio University of Helsinki

Functional Analysis mathscidoc:1803.43011

Arkiv for Matematik, 55, 2017
Moduli of path families are widely used to mark curves which may be neglected for some applications. We introduce ordinary and approximation modulus with respect to Banach function spaces. While these moduli lead to the same result in reflexive spaces, we show that there are important path families (like paths tangent to a given set) which can be labeled as negligible by the approximation modulus with respect to the Lorentz Lp,1-space for an appropriate p, in particular, to the ordinary L1-space if p=1, but not by the ordinary modulus with respect to the same space.
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@inproceedings{vendula2017modulus,
  title={Modulus in Banach function spaces},
  author={Vendula Honzlová Exnerová, Jan Malý, and Olli Martio},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180301155043873820946},
  booktitle={Arkiv for Matematik},
  volume={55},
  year={2017},
}
Vendula Honzlová Exnerová, Jan Malý, and Olli Martio. Modulus in Banach function spaces. 2017. Vol. 55. In Arkiv for Matematik. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180301155043873820946.
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