Functional properties of rearrangement invariant spaces defined in terms of oscillations

Joaquim Martín, María J. Carro, Amiran Gogatishvili, Luboš Pick

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

Abstract

Function spaces whose definition involves the quantity f** - f*, which measures the oscillation of f*, have recently attracted plenty of interest and proved to have many applications in various, quite diverse fields. Primary role is played by the spaces S p (w), with 0 < p < ∞ and w a weight function on (0, ∞), defined as the set of Lebesgue-measurable functions on ℝ such that f* (∞) = 0 and ∥f∥ S p (w):= (∫ 0∞ (f**(s) - f*(s)) p w(s)ds) 1/p < ∞. Some of the main open questions concerning these spaces relate to their functional properties, such as their lattice property, normability and linearity. We study these properties in this paper. © 2005 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)375-404
JournalJournal of Functional Analysis
Volume229
DOIs
Publication statusPublished - 15 Dec 2005

Keywords

  • Decreasing rearrangement
  • Distribution function
  • Lattice property
  • Normability

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