AbstractIn this paper, we consider the martingale Hardy spaces defined with the help of the mixed $$L_{\overrightarrow{p}}$$ L p → -norm. Five mixed martingale Hardy spaces will be investigated: $$H_{\overrightarrow{p}}^{s}$$ H p → s , $$H_{\overrightarrow{p}}^S$$ H p → S , $$H_{\overrightarrow{p}}^M$$ H p → M , $$\mathcal {P}_{\overrightarrow{p}}$$ P p → , and $$\mathcal {Q}_{\overrightarrow{p}}$$ Q p → . Several results are proved for these spaces, like atomic decompositions, Doob’s inequality, boundedness, martingale inequalities, and the generalization of the well-known Burkholder–Davis–Gundy inequality.