BMO with respect to Banach function spaces

Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi

Research output: Contribution to journalArticlepeer-review


For every cube Q⊂Rn we let XQ be a quasi-Banach function space over Q such that ‖χQ‖XQ≃1, and for X={XQ} define (Formula presented.) We study necessary and sufficient conditions on X such that (Formula presented.) In particular, we give a full characterization of the embedding BMO↪BMOX in terms of so-called sparse collections of cubes and we give easily checkable and rather weak sufficient conditions for the embedding BMOX↪BMO. Our main theorems recover and improve all previously known results in this area.

Original languageEnglish
Pages (from-to)4053-4082
Number of pages30
JournalMathematische Annalen
Issue number4
StatePublished - Apr 2024


  • 42B20
  • 42B25
  • 42B35
  • 46E30

All Science Journal Classification (ASJC) codes

  • General Mathematics


Dive into the research topics of 'BMO with respect to Banach function spaces'. Together they form a unique fingerprint.

Cite this