The space JNp : Nontriviality and duality

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http://hdl.handle.net/10138/315207

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Dafni , G , Hytönen , T , Korte , R & Yue , H 2018 , ' The space JNp : Nontriviality and duality ' , Journal of Functional Analysis , vol. 275 , no. 3 , pp. 577-603 . https://doi.org/10.1016/j.jfa.2018.05.007

Title: The space JNp : Nontriviality and duality
Author: Dafni, Galia; Hytönen, Tuomas; Korte, Riikka; Yue, Hong
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2018-08-01
Language: eng
Number of pages: 27
Belongs to series: Journal of Functional Analysis
ISSN: 0022-1236
URI: http://hdl.handle.net/10138/315207
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′.
Subject: Bounded mean oscillation
John–Nirenberg inequality
Atomic decomposition
Duality
SELF-IMPROVING PROPERTIES
JOHN-NIRENBERG
SETS
John-Nirenberg inequality
BOUNDED MEAN-OSCILLATION
POINCARE INEQUALITIES
BMO-TYPE NORMS
PERIMETER
111 Mathematics
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