Weighted norm inequalities for multisublinear maximal operator in martingale spaces

Abstract

Let $v, \omega_1, \omega_2$ be weights and let $1<p_1, p_2<\infty$. Suppose that $1/p=1/p_1+1/p_2$ and the couple of weights $(\omega_1,\omega_2)$ satisfies the reverse Hölder's condition. For the multisublinear maximal operator $\mathfrak{M}$ on 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 $L^{p,\infty}(v)$ or $L^p(v)$. If $v=\omega_2^{p/p_2}\omega_2^{p/p_2},$ we partially give the bilinear version of one-weight theory.