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 Cesàro means are bounded from the dyadic Hardy-Lorentz space pHra(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 ≤∞) 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 theinterpolation spaces between weak martingale Hardy spaces and martingale Hardy spaces.
