Characterization of Banach function spaces that preserve the Burkholder square-function inequality
The author considers Banach function space \(X\) over a nonatomic probability space. It is proved that the quadratic function of the uniformly integrable martingale \(f\) is equivalent to \(\lim_{n\to \infty}f_n \) if and only if the space \(X\) is rearrangement-invariant and can be renormed with an equivalent rearrangement-invariant norm satisfying some restrictions on its Boyd indices.
scientific article; zbMATH DE number 1993668