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Zeitschrift für Analysis und ihre Anwendungen


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Volume 40, Issue 1, 2021, pp. 1–32
DOI: 10.4171/ZAA/1670

Published online: 2021-01-25

The Equivalence Theorem for Logarithmic Interpolation Spaces in the Quasi-Banach Case

Blanca F. Besoy[1] and Fernando Cobos[2]

(1) Universidad Politécnica de Madrid, Spain
(2) Universidad Complutense de Madrid, Spain

We study the description by means of the $J$-functional of logarithmic interpolation spaces $(A_0, A_1)_{1,q,\mathbb{A}}$ in the category of the $p$-normed quasi-Banach couples ($0 < p \leq 1$). When $(A_0, A_1)$ is a Banach couple, it is known that the description changes depending on the relationship between $q$ and $\mathbb{A}$. In our more general setting, the parameter $p$ also has an important role as the results show.

Keywords: Logarithmic interpolation spaces, J-functional, K-functional, characteristic function

Besoy Blanca, Cobos Fernando: The Equivalence Theorem for Logarithmic Interpolation Spaces in the Quasi-Banach Case. Z. Anal. Anwend. 40 (2021), 1-32. doi: 10.4171/ZAA/1670