Modular Interpolation Spaces I

Abstract

An interpolation method in modular spaces is introduced and basic properties of obtained interpolation spaces are studied (completness, imbeddings etc.). The main result hero is a reiteration theorem. It is shown how the method works in Orlicz spaces and as an example of applications there is proved a multiplier theorem of the Michlin type. The method generalizes the $K$-method of Peetre.