Minimal conditions for BMO

2020/07/20 by Javier Canto, Carlos Pérez, Canto, Javier +3
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · doi:10.48550/arxiv.2007.10104

openalex publication_date 2020/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study minimal integrability conditions via Luxemburg-type expressions with respect to generalized oscillations that imply the membership of a given function f to the space BMO. Our method is simple, sharp and flexible enough to be adapted to several different settings, like spaces of homogeneous type, non doubling measures on ℝⁿ and also BMO spaces defined over more general bases than the basis of cubes.

Citations

• On functions of bounded mean oscillation

Related

• BMO: Oscillations, self improvement, Gagliardo coordinate spaces and reverse Hardy inequalities
• A characterization of Calderón-Zygmund operators on RBMO
• Boundedness of variation, oscillation and maximal differential transform on BMO space
• Dyadic-BMO functions, the dyadic Gurov-Reshetnyak conditions on\n [0,1]ⁿ and rearrangements of functions
• The John-Nirenberg space: Equality of the vanishing subspaces VJN_p and CJN_p