Characterization of interpolation between Grand, small or classical Lebesgue spaces

被引：31

作者：

Fiorenza, Alberto ^{[1
,2
]}

Formica, Maria Rosaria ^{[3
]}

Gogatishvili, Amiran ^{[4
]}

Kopaliani, Tengiz ^{[5
]}

Rakotoson, Jean Michel ^{[6
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Architettura, Via Monteoliveto 3, I-80134 Naples, Italy

[2] CNR, Ist Applicaz Calcolo Mauro Picone, Via Pietro Castellino 111, I-80131 Naples, Italy

[3] Univ Napoli Parthenope, Via Gen Parisi 13, I-80132 Naples, Italy

[4] Czech Acad Sci Zitna, Inst Math, Prague 11567 1, Czech Republic

[5] Javakhishvili Tbilisi State Univ, Fac Exact & Nat Sci, Univ St 2, GE-0143 Tbilisi, Georgia

[6] Univ Poitiers, Lab Math & Applicat, Ave Marie & Pierre Curie,Teleport 2,BP 30179, F-86692 Futuroscope, France

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2018年 / 177卷

基金：

美国国家科学基金会;

关键词：

REAL INTERPOLATION; DUALITY;

D O I：

10.1016/j.na.2017.09.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 Gamma-spaces. As a direct consequence of our results any Lorentz-Zygmund space L-a,L-r (Log L)(beta), is an interpolation space in the sense of Peetre between either two Grand Lebesgue spaces or between two small spaces provided that 1 < a < infinity, beta not equal 0. The method consists in computing the so called K-functional of the interpolation space and in identifying the associated norm. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：422 / 453

页数：32

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