Characterization of interpolation between Grand, small or classical Lebesgue spaces

2017/09/18 by Fiorenza, Aberto, Formica, Maria Rosaria, Gogatishvili, Amiran +2
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1709.05892

Abstract

In this paper, we show that the interpolation spaces between Grand, small or classical Lebesgue are so called Lorentz-Zygmund spaces or more generally GΓ-spaces. As a direct consequence of our results any Lorentz-Zygmund space L^a,r(\rm Log L)^β, is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or between two small spaces provided that 1

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