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 IA,m & OHM;,& alpha; with rough kernels & OHM; & ISIN; Ls(Sn-1), s > n/(n - & alpha;) on the variable exponent local general-ized Morrey spaces M{x0} p(& BULL;),& phi;, variable exponent generalized Morrey spaces Mp(& BULL;),& phi; and variable exponent vanishing generalized Morrey spaces VMp(& BULL;),& phi;, where the functions A belong to ho-mogeneous Lipschitz space ?& beta;, 0 < & beta; < 1.