Weighted weak type mixed \(\Phi\)-inequalities for martingale maximal operator

In this article, some necessary and sufficient conditions areshown for weighted weak type mixed \(\Phi\) $\mathrm{\Phi }$ -inequality and weighted extra-weak typemixed \(\Phi\) $\mathrm{\Phi }$ -inequality for martingale maximal operator. The obtained results generalizesome existing statements.