The space JNp

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2018-08-01
Major/Subject
Mcode
Degree programme
Language
en
Pages
27
577-603
Series
Journal of Functional Analysis, Volume 275, issue 3
Abstract
We study a function space JNp based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that Lp⊂JNp⊊Lp,∞, but otherwise the structure of JNp is largely a mystery. Our first main result is the construction of a function that belongs to JNp but not Lp, showing that the two spaces are not the same. Nevertheless, we prove that for monotone functions, the classes JNp and Lp do coincide. Our second main result describes JNp as the dual of a new Hardy kind of space HKp′ .
Description
Keywords
Atomic decomposition, Bounded mean oscillation, Duality, John–Nirenberg inequality, SELF-IMPROVING PROPERTIES, BOUNDED MEAN-OSCILLATION, BMO-TYPE NORMS, JOHN-NIRENBERG, POINCARE INEQUALITIES, PERIMETER, SETS
Other note
Citation
Dafni , G , Hytönen , T , Korte , R & Yue , H 2018 , ' The space JN p : Nontriviality and duality ' , Journal of Functional Analysis , vol. 275 , no. 3 , pp. 577-603 . https://doi.org/10.1016/j.jfa.2018.05.007