Logarithmic Interpolation Spaces Between Quasi-Banach Spaces

Abstract

Let A0 and A1 be quasi-Banach spaces with A0 ,! A1. By means of a direct approach, we show that the interpolation spaces on (A0;A1) generated by the function parameter tµ(1 + j log tj)¡b can be expressed in terms of classical real inter-polation spaces. Applications are given to Zygmund spaces Lp(log L)b(­), Lorentz-Zygmund function spaces and operator spaces de¯ned by using approximation num- bers.