JournalszaaVol. 26 , No. 1DOI 10.4171/zaa/1311

Logarithmic Interpolation Spaces between Quasi-Banach Spaces

  • Fernando Cobos

    Universidad Complutense de Madrid, Spain
  • Luz M. Fernández-Cabrera

    Universidad Complutense de Madrid, Spain
  • Antonio Manzano

    Escuela Politécnica Superior, Burgos, Spain
  • Antón Martínez

    E.T.S. Ingenieros Industriales, Vigo, Spain
Logarithmic Interpolation Spaces between Quasi-Banach Spaces cover

Abstract

Let A0A_0 and A1A_1 be quasi-Banach spaces with A0A1A_0 \hookrightarrow A_1. By means of a direct approach, we show that the interpolation spaces on (A0,A1)(A_0,A_1) generated by the function parameter tθ(1+logt)bt^\theta ( 1 + |\log t|)^{-b} can be expressed in terms of classical real interpolation spaces. Applications are given to Zygmund spaces Lp(logL)b(Ω)L_p (\log L)_b (\Omega), Lorentz-Zygmund function spaces and operator spaces defined by using approximation numbers.