Estimates for iterated commutators of multilinear square fucntions with Dini-type kernels

Abstract

Abstract Let TΠb→ $T_{\Pi\vec {b}}$ be the commutator generated by a multilinear square function and Lipschitz functions with kernel satisfying Dini-type condition. We show that TΠb→ $T_{\Pi\vec {b}}$ is bounded from product Lebesgue spaces into Lebesgue spaces, Lipschitz spaces, and Triebel–Lizorkin spaces.

Keywords

• Multilinear square fucntions
• Triebel–Lizorkin spaces
• Lipschitz spaces
• Iterated commutators