Holmstedt's formula for the K-functional: the limit case θ0=θ1

0579223 - MÚ 2024 RIV DE eng J - Článek v odborném periodiku
Ahmed, I. - Fiorenza, A. - Gogatishvili, Amiran
Holmstedt's formula for the K-functional: the limit case θ0=θ1.
Mathematische Nachrichten. Roč. 296, č. 12 (2023), s. 5474-5492. ISSN 0025-584X. E-ISSN 1522-2616
Grant CEP: GA ČR(CZ) GA23-04720S
Institucionální podpora: RVO:67985840
Klíčová slova: Holmstedt's formula * K-functional * K-interpolation spaces * slowly varying functions
Obor OECD: Pure mathematics
Impakt faktor: 1, rok: 2022
Způsob publikování: Open access
https://doi.org/10.1002/mana.202200440

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 & ISIN,{0,1}$\theta _0=\theta _1\in \lbrace 0,1\rbrace$. We also study the case & theta,0=& theta,1 & ISIN,(0,1)$\theta _0=\theta _1\in (0,1)$. Applications are given to Lorentz-Karamata spaces, generalized gamma spaces, and Besov spaces.
Trvalý link: https://hdl.handle.net/11104/0348075