Multilinear Maximal Operators on Triebel–Lizorkin Spaces and Besov Spaces

Abstract

In the present paper, the authors systematically study the mapping properties of multilinear maximal operators on the Triebel–Lizorkin spaces and Besov spaces. In the global setting, the authors provide a criterion on the boundedness and continuity of a class of multilinear operators on the Triebel–Lizorkin spaces and Besov spaces, which can be used to obtain the boundedness and continuity of the multilinear operators associated to balls, cubes and dyadic cubes, multilinear sharp maximal operator as well as multilinear operators of convolution type on the Triebel–Lizorkin spaces and Besov spaces. The corresponding results for the multilinear maximal operators associated to balls are also proved in the local setting.