Holmstedt's formula for the K-functional: the limit case θ0=θ1
Abstract
We consider K-interpolation spaces involving slowly varying functions, and derive necessary and sufficient conditions for a Holmstedt-type formula to be held in the limiting case θ0=θ1∈\0,1\. We also study the case θ0=θ1∈ (0,1). Applications are given to Lorentz-Karamata spaces, generalized gamma spaces and Besov spaces.
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