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Zeitschrift für Analysis und ihre Anwendungen


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Volume 26, Issue 1, 2007, pp. 65–86
DOI: 10.4171/ZAA/1311

Published online: 2007-03-31

Logarithmic Interpolation Spaces between Quasi-Banach Spaces

Fernando Cobos[1], Luz M. Fernández-Cabrera[2], Antonio Manzano[3] and Antón Martínez[4]

(1) Universidad Complutense de Madrid, Spain
(2) Universidad Complutense de Madrid, Spain
(3) Escuela Politécnica Superior, Burgos, Spain
(4) E.T.S. Ingenieros Industriales, Vigo, Spain

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.

Keywords: Logarithmic interpolation spaces, real interpolation with a parameter function, Zygmund function spaces, Lorentz-Zygmund function spaces, operator spaces defined by using approximation numbers

Cobos Fernando, Fernández-Cabrera Luz, Manzano Antonio, Martínez Antón: Logarithmic Interpolation Spaces between Quasi-Banach Spaces. Z. Anal. Anwend. 26 (2007), 65-86. doi: 10.4171/ZAA/1311