A note on the energy inequalities for increasing processes
The best estimation of a ratio inequality for continuous martingales
Improved ratio inequalities for martingales
On a relation between norms of the maximal function and the square function of a martingale
Let Ω be a nonatomic probability space, let X be a Banach function space over Ω, and let ℳ be the collection of all martingales on Ω. For , let Mf and Sf denote the maximal function and the square function of f, respectively. We give some necessary and sufficient conditions for X to have the property that if f, g ∈ ℳ and , then , where C is a constant independent of f and g.
On some mean oscillation inequalities for martingales.
Some remarks on ratio inequalities for continuous martingales
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