Multilinear strongly singular integral operators with generalized kernels and applications

Abstract

In this paper, the authors study the boundedness properties of a class of multilinear strongly singular integral operator with generalized kernels on product of weighted Lebesgue spaces and product of variable exponent Lebesgue spaces, respectively. Moreover, the types $ L^{\infty}\times \dots \times L^{\infty}\rightarrow BMO $ and $ BMO\times \dots \times BMO\rightarrow BMO $ endpoint estimates are also obtained.

Keywords

• multilinear strongly singular integral operator with generalized kernel
• sharp maximal function
• bmo function
• weighted lebesgue space
• variable exponent lebesgue space