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 / D'Onofrio, L.; Greco, L.; Perfekt, K. -M.; Sbordone, C.; Schiattarella, R.. - In: ANNALES DE L INSTITUT HENRI POINCARÉ. ANALYSE NON LINÉAIRE. - ISSN 0294-1449. - (2020). [10.1016/j.anihpc.2020.01.004]
Atomic decompositions, two stars theorems, and distances for the Bourgain–Brezis–Mironescu space and other big spaces
Greco L.;Sbordone C.;Schiattarella R.
2020
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
