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A new Brézis‐Gallouët‐Wainger inequality from the viewpoint of the real interpolation functors
Author(s) -
Sawano Yoshihiro
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.201100324
Subject(s) - mathematics , pure mathematics , embedding , functor , interpolation (computer graphics) , inequality , property (philosophy) , logarithm , mathematical analysis , image (mathematics) , artificial intelligence , computer science , philosophy , epistemology
The Brézis‐Gallouët‐Wainger inequality describes a subtle embedding property into L ∞ . The relation between the Brézis‐Gallouët‐Wainger inequality and the real interpolation functor together with the sharpness of the results is discussed in the present paper. As our first main results shows, it turns out that there are two intermediate terms between L ∞ and the logarithmic boundedness, which is supposed to be the right‐hand side of the Brézis‐Gallouët‐Wainger inequality. As the second result, the first result is extended to inequalities which reflect the meaning of the second index of Besov spaces and the interpolation theorem.