Logarithmic Interpolation Spaces between Quasi-Banach Spaces

Fernando Cobos; Luz M. Fernández-Cabrera; Antonio Manzano; Antón Martínez

doi:10.4171/zaa/1311

JournalszaaVol. 26, No. 1pp. 65–86

Logarithmic Interpolation Spaces between Quasi-Banach Spaces

Fernando Cobos
Universidad Complutense de Madrid, Spain
MathSciNet ORCID
Luz M. Fernández-Cabrera
Universidad Complutense de Madrid, Spain
MathSciNet ORCID
Antonio Manzano
Escuela Politécnica Superior, Burgos, Spain
MathSciNet zbMATH Open
Antón Martínez
E.T.S. Ingenieros Industriales, Vigo, Spain
MathSciNet ORCID

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Abstract

Let $A_{0}$ and $A_{1}$ be quasi-Banach spaces with $A_{0} ↪ A_{1}$ . By means of a direct approach, we show that the interpolation spaces on $(A_{0}, A_{1})$ generated by the function parameter $t^{θ} (1 + ∣ lo g t ∣)^{- b}$ can be expressed in terms of classical real interpolation spaces. Applications are given to Zygmund spaces $L_{p} (lo g L)_{b} (Ω)$ , Lorentz-Zygmund function spaces and operator spaces defined by using approximation numbers.

Cite this article

Fernando Cobos, Luz M. Fernández-Cabrera, Antonio Manzano, Antón Martínez, Logarithmic Interpolation Spaces between Quasi-Banach Spaces. Z. Anal. Anwend. 26 (2007), no. 1, pp. 65–86

DOI 10.4171/ZAA/1311