Weighted norm inequalities for multisublinear maximal operator in martingale spaces

Let $v,{\omega }_1,{\omega }_2$ be weights and $1<p_1,p_2<\mathrm{\infty }\mathrm{.}$ Suppose that $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ and $(\omega_1, \omega_2)\in RH(p_1, p_2).$Forthemultisublinearmaximaloperator$\mathfrak{M}$ in martingale spaces, we characterize the weights for which $\mathfrak{M}$ is bounded from $L^{p_1}({\omega }_1)\times L^{p_2}({\omega }_2)$ to $L^{p,\mathrm{\infty }}(v)\text{or}{L}^p(v)\mathrm{.}$ If $v={\omega }_2^{\frac{p}{p_2}}{\omega }_2^{\frac{p}{p_2}},$ we partially give the bilinear version of one-weight theory.