Logarithmic Interpolation Spaces between Quasi-Banach Spaces

Abstract

Let $A_0$ and $A_1$ be quasi-Banach spaces with $A_0 \hookrightarrow A_1$. By means of a direct approach, we show that the interpolation spaces on $(A_0,A_1)$ generated by the function parameter $t^\theta ( 1 + |\log t|)^{-b}$ can be expressed in terms of classical real interpolation spaces. Applications are given to Zygmund spaces $L_p (\log L)_b (\Omega)$, Lorentz-Zygmund function spaces and operator spaces defined by using approximation numbers.