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

We obtain the Lipschitz boundedness for a class of fractional multilinear integral operators IΩ,αA,m with rough kernels Ω∈Ls(𝕊n−1), s>n/(n−α) on the variable exponent local generalized Morrey spaces Mp(·),φ{x0}, variable exponent generalized Morrey spaces Mp(·),φ and variable exponent vanishing generalized Morrey spaces VMp(·),φ, where the functions A belong to homogeneous Lipschitz space Λ˙β, 0≤β≤1.