BMO with respect to Banach function spaces

Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi

Research output: Contribution to journalArticlepeer-review

Abstract

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
Volume388
Issue number4
DOIs
StatePublished - Apr 2024

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

Funding

Andrei K. Lerner was supported by ISF Grant no. 1035/21. Emiel Lorist was supported by the Academy of Finland through Grant no. 336323. Sheldy Ombrosi was partially supported by ANPCyT PICT 2018-2501.

FundersFunder number
Academy of Finland336323
Agencia Nacional de Promoción Científica y TecnológicaPICT 2018-2501
Israel Science Foundation1035/21

    Keywords

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

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