In this article, the Banach space X and the martingales with values in it are considered. It is shown that the maximal operators of the one-dimensional dyadic derivative of the dyadic integral and Cesaro means are bounded from the dyadic Hardy- Lorentz space pH^-ra(X) to Lra(X) when X is isomorphic to a p-uniformly smooth space (1 〈p ≤ 2). And it is also bounded from Hra(X) to Lra(X) (0 〈 r 〈 ∞,0 〈 a≤oc) when X has Radon-Nikodym property. In addition, some weak-type inequalities are given.
By the weak atomic decompositions of weak martingale Hardy spaces, we investigate the interpolation spaces between weak martingale Hardy spaces and martingale Hardy spaces.