English

Holmstedt's formula for the $K$-functional: the limit case $\theta_0=\theta_1$

Functional Analysis 2022-10-25 v1

Abstract

We consider KK-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\{0,1\}. 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.

Keywords

Cite

@article{arxiv.2210.12377,
  title  = {Holmstedt's formula for the $K$-functional: the limit case $\theta_0=\theta_1$},
  author = {Irshaad Ahmed and Alberto Fiorenza and Amiran Gogatishvili},
  journal= {arXiv preprint arXiv:2210.12377},
  year   = {2022}
}