# Mean oscillation and boundedness of multilinear integral operators with general kernels

## Liu Lanzhe

Address: Department of Mathematics, Hunan University, Changsha 410082, P. R. of China

E-mail: lanzheliu@163.com

Abstract: In this paper, the boundedness properties for some multilinear operators related to certain integral operators from Lebesgue spaces to Orlicz spaces are proved. The integral operators include singular integral operator with general kernel, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator.

AMSclassification: primary 42B20; secondary 42B25.

Keywords: multilinear operator, singular integral operator, BMO space, Orlicz space, Littlewood-Paley operator, Marcinkiewicz operator, Bochner-Riesz operator.

DOI: 10.5817/AM2014-2-77