Boundedness of multilinear operators on generalized Morrey spaces

Abstract

In this paper, the authors prove the boundedness of the multilinear maximal functions, multilinear singular integrals and multilinear Riesz potential on the product generalized Morrey spaces $\mathcal{M}_{p_1 ,\omega _1 } (\mathbb{R}^n ) \times \cdots \times \mathcal{M}_{p_m ,\omega _1 } (\mathbb{R}^n )$ respectively. The main theorems of this paper extend some known results.