Weighted norm inequalities for multisublinear maximal operator in martingale spaces

Abstract

Let $v,{\omega }_1,{\omega }_2$ be weights and $1<p_1,p_2<\infty .$ Suppose that $\frac{1}{p}=\frac{1}{p_1}+\frac{1}{p_2}$ and $({\omega }_1,{\omega }_2)\in RH(p_1,p_2).$ For the multisublinear maximal operator $\mathfrak{M}$ 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 $L^{p,\infty }(v)or{L}^p(v).$ If $v={\omega }_2^{\frac{p}{p_2}}{\omega }_2^{\frac{p}{p_2}},$ we partially give the bilinear version of one-weight theory.

15 pages

References in corpus (2)

• The multilinear strong maximal function
• Weighted estimates for the multilinear maximal function

Cited by in corpus (1)

• Weighted estimates for the multilinear maximal function