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 language | English |
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Pages (from-to) | 4053-4082 |
Number of pages | 30 |
Journal | Mathematische Annalen |
Volume | 388 |
Issue number | 4 |
DOIs | |
State | Published - 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.
Funders | Funder number |
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Academy of Finland | 336323 |
Agencia Nacional de Promoción Científica y Tecnológica | PICT 2018-2501 |
Israel Science Foundation | 1035/21 |
Keywords
- 42B20
- 42B25
- 42B35
- 46E30