Boundedness and Compactness of Multilinear Singular Integrals on Morrey Spaces

Abstract

In this paper, we consider the boundedness and compactness of the multilinear singular integral operator on Morrey spaces, which is defined by $$T_Af(x)={\rm p.v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}R(A;x,y)f(y)dy,$$ where $R(A;x,y)=A(x)−A(y)−∇A(y)·(x−y)$ with $D^βA∈BMO(\mathbb{R}^n)$ for all $|β|=1.$ We prove that $T_A$ is bounded and compact on Morrey spaces $L^{p,λ}(\mathbb{R}^n)$ for all $1