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

D'Onofrio, L., Greco, L., Perfekt, K.-M., Sbordone, C. and Schiattarella, R. (2020) Atomic decompositions, two stars theorems, and distances for the Bourgain-Brezis-Mironescu space and other big spaces. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 37 (3). pp. 653-661. ISSN 0294-1449

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To link to this item DOI: 10.1016/j.anihpc.2020.01.004

Abstract/Summary

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∈B to B0 .

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:88445
Publisher:Elsevier

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