Endpoint estimates for multilinear fractional integrals with non-doubling measures

Abstract

Under the assumption that µ is a non-doubling measure on ℝd which only satisfies the polynomial growth condition, the authors obtain the boundedness of the multilinear fractional integrals on Morrey spaces, weak-Morrey spaces and Lipschitz spaces associated with µ, which, in the case when µ is the d-dimensional Lebesgue measure, also improve the known results.