Characterization of interpolation between Grand, small or classical Lebesgue spaces

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 La,r(LogL)β, is an interpolation space in the sense of Peetre between eit...

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Published inNonlinear analysis Vol. 177; pp. 422 - 453
Main Authors Fiorenza, Alberto, Formica, Maria Rosaria, Gogatishvili, Amiran, Kopaliani, Tengiz, Rakotoson, Jean Michel
Format Journal Article
LanguageEnglish
Published Elmsford Elsevier Ltd 01.12.2018
Elsevier BV
Subjects
Interpolation
Linear equations
Mathematical analysis
Studies
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Summary: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 La,r(LogL)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.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2017.09.005