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In this paper, we study the boundedness of fractional multilinear integral operators with rough kernels [...] TΩ,αA1,A2,…,Ak, $T_{\Omega ,\alpha }^{A_1,A_2,...,A_k},$ which is a generalization of the higher-order commutator of the rough fractional integral on the generalized weighted Morrey spaces Mp,ϕ (w). We find the sufficient conditions on the pair (ϕ1, ϕ2) with w ∈ Ap,q which ensures the boundedness of the operators [...] TΩ,αA1,A2,…,Ak, $T_{\Omega ,\alpha }^{A_1,A_2,...,A_k},$ from [...] Mp,φ1wptoMp,φ2wq $M_{p,{\varphi }_1}\left(w^p\right)\mathrm{to}{M}_{p,{\varphi }_2}\left(w^q\right)$ for 1 < p < q < ∞. In all cases the conditions for...

In the paper we find conditions on the pair $({\omega }_1,{\omega }_2)$ which ensure the boundedness of the maximal operator and the Calderón-Zygmund singular integral operators from one generalized Morrey space ${ℳ}_{p,{\omega }_1}$ to another ${ℳ}_{p,{\omega }_2}$, $1<p<\infty$, and from the space ${ℳ}_{1,{\omega }_1}$ to the weak space $W{ℳ}_{1,{\omega }_2}$. As applications, we get some estimates for uniformly elliptic operators on generalized Morrey spaces.