Weak compactness and convergence in two-parameter martingale Hardy spaces and the dual of the VMO space.
Weak type estimates associated to Burkholder's martingale inequality.
Weak Type Inequality for the Square Function of a Nonnegative Submartingale
Let f be a nonnegative submartingale and S(f) denote its square function. We show that for any λ > 0, , and the constant π/2 is the best possible. The inequality is strict provided ∥f∥₁ ≠ 0.