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...

We consider the Dirac-type operators D + a, a is a paravector in the Clifford algebra. For this operator we state a Cauchy-Green formula in the spaces $C^1\left(G\right)$ and $W_p^1\left(G\right)$. Further, we consider the Cauchy problem for this operator.