Holmstedt's formula for the $K$-functional: the limit case $θ_0=θ_1$

Published 22 Oct 2022 in math.FA | (2210.12377v1)

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 $\theta_0=\theta_1\in{0,1}.$ We also study the case $\theta_0=\theta_1\in (0,1).$ Applications are given to Lorentz-Karamata spaces, generalized gamma spaces and Besov spaces.

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