On interpolation and 𝐾-monotonicity for discrete local Morrey spaces

Abstract

A formula is given that makes it possible to reduce the calculation of an interpolation functor on a pair of local Morrey spaces to the calculation of this functor on pairs of vector function spaces constructed from the ideal spaces involved in the definition of the Morrey spaces in question. It is shown that a pair of local Morrey spaces is K K -monotone if and only if the pair of vector function spaces mentioned above is K K -monotone. This reduction makes it possible to obtain new interpolation theorems even for classical local spaces.