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 B0⁎=B⁎ and B⁎⁎=B, and a formula for the distance from an element f∈B to B0.

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

Sbordone C.;
2020-01-01

Abstract

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 B0⁎=B⁎ and B⁎⁎=B, and a formula for the distance from an element f∈B to B0.
2020
Atomic decomposition
Bourgain-Brezis-Mironescu space
Dual and predual
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12570/17714
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
social impact