Characterization of interpolation between Grand, small or classical Lebesgue spaces. (December 2018) - Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran; Kopaliani, Tengiz; Rakotoson, Jean Michel
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 G Γ -spaces. As a direct consequence of our results any Lorentz–Zygmund space L a, r ( 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 < a < ∞, β ≠ 0 . The method consists in computing the so called K-functional of the interpolation space and in identifying the associated norm.