Multi-sublinear rough fractional maximal operator on product modified Morrey spaces

We will study the boundedness of multi-sublinear fractional maximal operator $\M_{\Omega,\a,m}$ with rough kernels $\Omega\in L^s(\mathbb{S}^{mn-1})$, $1<s\leq\i$ on product modified Morrey spaces. We find for the operator $\M_{\Omega,\a,m}$ necessary and sufficient conditions on the parameters of the boundedness on product modified Morrey spaces $\widetilde{L}^{p_1,\lambda_1}(\Rn) \times \ldots \times \widetilde{L}^{p_m,\lambda_m}(\Rn)$ to modified Morrey spaces $\widetilde{L}^{q,\lambda}(\Rn)$.