The K-functional and reiteration theorems for Left and Right spaces, Part II

Abstract

We consider the K-interpolation methods involving slowly varying functions. Let A‾θ,⁎L and A‾θ,⁎R (0≤θ≤1) be the so-called L or R limiting interpolation spaces which arise naturally in reiteration formulae for the limiting cases. We characterize the interpolation spaces (X,Y)θ,r,a (0≤θ≤1), where X=A‾θ0,⁎L or X=A‾θ0,⁎R and Y=A‾θ1,⁎L or Y=A‾θ1,⁎R, provided that 0≤θ0<θ1≤1 and at least one of the parameters θ0 or θ1 has the limiting value θ0=0 or θ1=1. This supplements the first part of the paper, where one of the operands is standard interpolation spaces involving slowly varying functions. The proofs of most reiteration theorems are based on Holmstedt-type formulae. Applications to grand and small Lorentz spaces are given.