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
@article{AIHPC_2020__37_3_653_0, author = {D'Onofrio, Luigi and Greco, Luigi and Perfekt, Karl-Mikael and Sbordone, Carlo and Schiattarella, Roberta}, title = {Atomic decompositions, two stars theorems, and distances for the {Bourgain{\textendash}Brezis{\textendash}Mironescu} space and other big spaces}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {653--661}, publisher = {Elsevier}, volume = {37}, number = {3}, year = {2020}, doi = {10.1016/j.anihpc.2020.01.004}, mrnumber = {4093624}, zbl = {1443.46005}, language = {en}, url = {https://www.numdam.org/articles/10.1016/j.anihpc.2020.01.004/} }
TY - JOUR AU - D'Onofrio, Luigi AU - Greco, Luigi AU - Perfekt, Karl-Mikael AU - Sbordone, Carlo AU - Schiattarella, Roberta TI - Atomic decompositions, two stars theorems, and distances for the Bourgain–Brezis–Mironescu space and other big spaces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2020 SP - 653 EP - 661 VL - 37 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2020.01.004/ DO - 10.1016/j.anihpc.2020.01.004 LA - en ID - AIHPC_2020__37_3_653_0 ER -
%0 Journal Article %A D'Onofrio, Luigi %A Greco, Luigi %A Perfekt, Karl-Mikael %A Sbordone, Carlo %A Schiattarella, Roberta %T Atomic decompositions, two stars theorems, and distances for the Bourgain–Brezis–Mironescu space and other big spaces %J Annales de l'I.H.P. Analyse non linéaire %D 2020 %P 653-661 %V 37 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2020.01.004/ %R 10.1016/j.anihpc.2020.01.004 %G en %F AIHPC_2020__37_3_653_0
D'Onofrio, Luigi; Greco, Luigi; Perfekt, Karl-Mikael; Sbordone, Carlo; Schiattarella, Roberta. Atomic decompositions, two stars theorems, and distances for the Bourgain–Brezis–Mironescu space and other big spaces. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 3, pp. 653-661. doi : 10.1016/j.anihpc.2020.01.004. https://www.numdam.org/articles/10.1016/j.anihpc.2020.01.004/
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