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Smoothness of the Orlicz norm in Musielak–Orlicz function spaces
Author(s) -
Vigelis Rui F.,
Cavalcante Charles C.
Publication year - 2014
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201200214
Subject(s) - mathematics , smoothness , norm (philosophy) , pure mathematics , function space , mathematical analysis , political science , law
In this paper, we present a characterization of support functionals and smooth points in L 0 Φ , the Musielak–Orlicz space equipped with the Orlicz norm. As a result, criterion for the smoothness of L 0 Φ is also obtained. Some expressions involving the norms of functionals in( L 0 Φ ) * , the topological dual of L 0 Φ , are proved for arbitrary Musielak–Orlicz functions.