The space JNp: Nontriviality and duality

Galia Dafni, Tuomas Hytönen, Riikka Korte*, Hong Yue

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)
16 Downloads (Pure)

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 .

Original languageEnglish
Pages (from-to)577-603
Number of pages27
JournalJournal of Functional Analysis
Volume275
Issue number3
DOIs
Publication statusPublished - 1 Aug 2018
MoE publication typeA1 Journal article-refereed

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

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