Atomic decompositions, two stars theorems, and distances for the Bourgain-Brezis-Mironescu space and other big spaces

被引：12

作者：

D'Onofrio, Luigi ^{[1
]}

Greco, Luigi ^{[2
]}

Perfekt, Karl-Mikael ^{[3
]}

Sbordone, Carlo ^{[4
]}

Schiattarella, Roberta ^{[4
]}

机构：

[1] Univ Napoli Parthenope, Ctr Direzionale Isola C4, Dipartimento Sci & Tecnol, Naples 80100, Italy

[2] Univ Napoli Federico II, Dipartimento Ingn Elettr & Tecnol Informaz, Via Claudio 21, Naples 80125, Italy

[3] Univ Reading, Dept Math & Stat, Reading RG6 6AX, Berks, England

[4] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia, Naples 80126, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2020年 / 37卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Dual and predual; Bourgain-Brezis-Mironescu space; Atomic decomposition;

D O I：

10.1016/j.anihpc.2020.01.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a Banach space E with a supremum-type norm induced by a collection of operators, we prove that E is a dual space and provide an atomic decomposition of its predual. We apply this result, and some results obtained previously by one of the authors, to the function space B introduced recently by Bourgain, Brezis, and Mironescu. This yields an atomic decomposition of the predual B-*, the biduality result that B-0* = B-* and B-** = B, and a formula for the distance from an element f is an element of B to B-0. (C) 2020 Elsevier Masson SAS. All rights reserved.

引用

页码：653 / 661

页数：9

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