Let (A0, A1) be a compatible pair of quasi-Banach spaces and 1etA be a corresponding space of real interpolation type such that A0∩A1 is not dense in A. Upper and lower estimates are obtained for the distance of any element f of A from A0∩A1. These lead to formulae for the distance in a large number of concrete situations, such as when A0∩A1=L∞ and A is either weak-Lq, a ‘grand’ Lebesgue space or an Orlicz space of exponential type.
"Formulae for the distance in some quasi-Banach spaces." Ark. Mat. 43 (1) 145 - 165, April 2005. https://doi.org/10.1007/BF02383616