Noncommutative weak-L∞ and BMO

Bennett et al. (Ann Math 113:601–611, 1981) introduced the weak analogue of the space L∞ and studied its relationship to the space of functions of bounded mean oscillation. The purpose of this paper is to continue this line of research in the context of functions on Rd with values in a finite von Ne...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Mathematische annalen Ročník 391; číslo 3; s. 3519 - 3553
Hlavní autori: Jiao, Yong, Osękowski, Adam, Wu, Lian, Zuo, Yahui
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Heidelberg Springer Nature B.V 01.03.2025
Predmet:
Algebra
Decomposition
Estimates
Harmonic analysis
Inequality
Martingales
Operators (mathematics)
ISSN:0025-5831, 1432-1807
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:Bennett et al. (Ann Math 113:601–611, 1981) introduced the weak analogue of the space L∞ and studied its relationship to the space of functions of bounded mean oscillation. The purpose of this paper is to continue this line of research in the context of functions on Rd with values in a finite von Neumann algebra. As a by-product, this allows for the comparison of the BMO norms of an operator-valued function and its decreasing rearrangement. The argument rests on a novel distributional estimate for noncommutative martingales invoking Cuculescu projections, which is of independent interest. The applications include related BMO→wL∞ inequalities for square functions and conditional square functions, as well as corresponding versions of Stein and dual Doob estimates, which are new even for classical martingales.
Bibliografia:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-024-03021-5