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

Abstract

We obtain the Lipschitz boundedness for a class of fractional multilinear integral operators $I_{\mathrm{\Omega },\alpha }^{A,m}$ with rough kernels $\mathrm{\Omega }\in L_s({𝕊}^{n-1})$, on the variable exponent local generalized Morrey spaces $M_{p(·),\phi }^{\left\{x_0\right\}}$, variable exponent generalized Morrey spaces $M_{p(·),\phi }$ and variable exponent vanishing generalized Morrey spaces $V{M}_{p(·),\phi }$, where the functions $A$ belong to homogeneous Lipschitz space ${\dot{\mathrm{\Lambda }}}_{\beta }$, $0\le \beta \le 1$.