Holmstedt's formula for the K‐functional: the limit case θ0=θ1$\theta _0=\theta _1$

Irshaad Ahmed, Alberto Fiorenza and Amiran Gogatishvili

Mathematische Nachrichten, 2023, vol. 296, issue 12, 5474-5492

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}$\theta _0=\theta _1\in \lbrace 0,1\rbrace$. We also study the case θ0=θ1∈(0,1)$\theta _0=\theta _1\in (0,1)$. Applications are given to Lorentz–Karamata spaces, generalized gamma spaces, and Besov spaces.

Date: 2023
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https://doi.org/10.1002/mana.202200440

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