# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc: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.
```@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.