B-valued martingale spaces with small index and atomic decompositions
Some atomic decomposition theorems for Banach-space-valued martingales are established. Using them, the embedding relationships between martingale spaces with small index are discussed. The results obtained here are closely connected with the \(p\)-uniform smoothness and \(q\)-uniform convexity of the Banach space in which the martingales take values.
scientific article; zbMATH DE number 1782053