BMO with respect to Banach function spaces

Andrei K. Lerner; Emiel Lorist; Sheldy Ombrosi

doi:10.1007/s00208-023-02628-4

BMO with respect to Banach function spaces

Andrei K. Lerner, Emiel Lorist, Sheldy Ombrosi

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

For every cube Q⊂Rⁿ we let X_Q be a quasi-Banach function space over Q such that ‖χ_Q‖X_Q≃1, and for X={X_Q} 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↪BMO_X in terms of so-called sparse collections of cubes and we give easily checkable and rather weak sufficient conditions for the embedding BMO_X^∗↪BMO. Our main theorems recover and improve all previously known results in this area.

Original language	English
Pages (from-to)	4053-4082
Number of pages	30
Journal	Mathematische Annalen
Volume	388
Issue number	4
DOIs	https://doi.org/10.1007/s00208-023-02628-4
State	Published - Apr 2024

Keywords

42B20
42B25
42B35
46E30

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00208-023-02628-4

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title = "BMO with respect to Banach function spaces",

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.",

keywords = "42B20, 42B25, 42B35, 46E30",

author = "Lerner, {Andrei K.} and Emiel Lorist and Sheldy Ombrosi",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2024",

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doi = "10.1007/s00208-023-02628-4",

language = "الإنجليزيّة",

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TY - JOUR

T1 - BMO with respect to Banach function spaces

AU - Lerner, Andrei K.

AU - Lorist, Emiel

AU - Ombrosi, Sheldy

PY - 2024/4

Y1 - 2024/4

N2 - 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.

AB - 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.

KW - 42B20

KW - 42B25

KW - 42B35

KW - 46E30

UR - http://www.scopus.com/inward/record.url?scp=85154590767&partnerID=8YFLogxK

U2 - 10.1007/s00208-023-02628-4

DO - 10.1007/s00208-023-02628-4

M3 - مقالة

SN - 0025-5831

VL - 388

SP - 4053

EP - 4082

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 4

ER -

BMO with respect to Banach function spaces

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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