### Lipschitz estimates for rough fractional multilinear integral operators on local generalized Morrey spaces

#### I. Ekincioglu, C. Keskin, R. V. Guliyev

We obtain the Lipschitz boundedness for a class of fractional multilinear operators $I_{\Omega,\alpha}^{A,m}$ with rough kernels $\Omega\in L_{s}(\S^{n-1})$, $s>n/(n-\alpha)$ on the local generalized Morrey spaces $LM_{p,\varphi}^{\{x_0\}}$, generalized Morrey spaces $M_{p,\varphi}$ and vanishing generalized Morrey spaces $VM_{p,\varphi}$, where the functions $A$ belong to homogeneous Lipschitz space $\dot{\Lambda}_{\beta}$, $0<\beta<1$. We find the sufficient conditions on the pair $(\varphi_1,\varphi_2)$ which ensures the boundedness of the operators $I_{\Omega,\alpha}^{A,m}$ from $LM_{p,\varphi_1}^{\{x_0\}}$ to $LM_{q,\varphi_2}^{\{x_0\}}$, from $M_{p,\varphi_1}$ to $M_{q,\varphi_2}$ and from $VM_{p,\varphi_1}$ to $VM_{q,\varphi_2}$ for \$1

Tbilisi Mathematical Journal, Vol. 13(1) (2020), pp. 47-60