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Martingale type, the Gamlen-Gaudet construction and a greedy algorithm.
- Source :
-
Journal of Functional Analysis . May2024, Vol. 286 Issue 9, pN.PAG-N.PAG. 1p. - Publication Year :
- 2024
-
Abstract
- In the present paper we identify those filtered probability spaces (Ω , F , (F n) , P) that determine already the martingale type of a Banach space X. We isolate intrinsic conditions on the filtration (F n) of purely atomic σ -algebras which determine that the upper ℓ p estimates ‖ f ‖ L p (Ω , X) p ⩽ C p (‖ E (f | F 0) ‖ L p (Ω , X) p + ∑ n = 1 ∞ ‖ E (f | F n) − E (f | F n − 1) ‖ L p (Ω , X) p) , f ∈ L p (Ω , X) imply that the Banach space X is of martingale type p. Our paper complements G. Pisier's investigation [12] and continues the work by S. Geiss and second named author in [3]. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00221236
- Volume :
- 286
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Functional Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 175981815
- Full Text :
- https://doi.org/10.1016/j.jfa.2024.110369