Characterization of interpolation between Grand, small or classical Lebesgue spaces. (December 2018)

• Record Type: Journal Article
• Authors: Fiorenza, Alberto; Formica, Maria Rosaria; Gogatishvili, Amiran; Kopaliani, Tengiz; Rakotoson, Jean Michel
• Is Part Of: Nonlinear analysis. Volume 177(2018)Part B
• Page Start: 422
• Page End: 453
• Publication Date: 2018-12
• Subjects: Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.09.005
• Languages: English
• ISSNs: 0362-546X

Abstract

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.