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.

中文翻译：

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拟Banach情况下对数插值空间的等价定理。

我们通过对数插值空间$（A_0，A_1）_ {1，q，\ mathbb {A}} $的$ J $函数来研究描述，该函数属于$ p $赋范格拟Banach夫妇（$ 0 <p \ leq 1 $）。当$（A_0，A_1）$是Banach夫妇时，已知描述会根据$ q $和$ \ mathbb {A} $之间的关系而变化。结果表明，在我们更一般的设置中，参数$ p $也起着重要作用。