Limiting reiteration for real interpolation with slowly varying functions

We present reiteration formulae with limiting values θ = 0 and θ = 1 for a real interpolation method involving slowly varying functions. Applications to the Lorentz–Karamata spaces, the Fourier transform and the Riesz potential are given. In particular, our results yield improvements of limiting Sobolev‐type embeddings due to Trudinger, Hansson, Brézis and Wainger, Edmunds, Gurka and Opic, Fusco, Lions and Sbordone, et al., and they are related to those of Edmunds, Kerman and Pick, or Pustylnik. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)