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

Abstract

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 ($0<p\le 1$). 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.