Sharp bounds for multilinear fractional integral operators on Morrey type spaces: the endpoint cases

Abstract

In this paper, the Strichartz’s result of the exponential integrability of fractional integral operators is improved. Also, we establish the endpoint boundedness of the multilinear fractional integrals acting on the multi-Morrey spaces. The conclusions relax the restriction that $$p_{i}\ne 1$$ for all $$i=1,\ldots ,m$$ and extend some known results.