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Formulae for the distance in some quasi-Banach spaces

David E. Edmunds Department of Mathematics, University of Sussex Georgi E. Karadzhov Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

TBD mathscidoc:1701.333051

Arkiv for Matematik, 43, (1), 145-165, 2003.5
Let ($A$_{$0, A$}_{$1$}) be a compatible pair of quasi-Banach spaces and 1et$A$be a corresponding space of real interpolation type such that$A$_{$0$}∩$A$_{$1$}is not dense in$A$. Upper and lower estimates are obtained for the distance of any element$f$of$A$from$A$_{$0$}∩$A$_{$1$}. These lead to formulae for the distance in a large number of concrete situations, such as when$A$_{$0$}∩$A$_{$1$}=$L$^{$∞$}and$A$is either weak-$L$^{q}, a ‘grand’ Lebesgue space or an Orlicz space of exponential type.
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@inproceedings{david2003formulae,
  title={Formulae for the distance in some quasi-Banach spaces},
  author={David E. Edmunds, and Georgi E. Karadzhov},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203613569672860},
  booktitle={Arkiv for Matematik},
  volume={43},
  number={1},
  pages={145-165},
  year={2003},
}
David E. Edmunds, and Georgi E. Karadzhov. Formulae for the distance in some quasi-Banach spaces. 2003. Vol. 43. In Arkiv for Matematik. pp.145-165. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203613569672860.
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