Commutators of multilinear Calderón–Zygmund operators with Dini type kernels on some function spaces

Abstract

In this paper, we establish some new boundedness for commutators of multilinear Calderón-Zygmund operators with kernels of type ω from product of Lebesgue spaces into Lebesgue spaces, Lipschitz spaces, and Triebel-Lizorkin spaces, which extend some previous results.

Iterated commutators of multilinear Calderón–Zygmund maximal operators on some function spaces

“…The multilinear analogues of the results in [17] were given by Wang and Xu [23] and by Mo and Lu [16]. Finally, Sun and Zhang [22] relaxed the smooth condition assumed on the kernel to Dini-type condition. It is natural to ask whether, under the Dini-type condition, the iterated commutators of multilinear Calderón-Zygmund maximal operators and pointwise multiplication with functions in Lipschitz space share similar boundedness properties?…”

“…The main ideas in this section are from [17] and [19]. We should also mention that the proof of this part is similar to that of Theorem 1.2 and Theorem 1.3 in [22]; we just give the different part of the proof. We begin with the proof of Theorem 1.2.…”

“…We borrow some ideas from [19]. Since the proof of Theorem 1.1 follows from similar steps in [22], we omit the proof. We just give three key lemmas.…”

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

“…By using Lemma 3.1 and modifying the proof of Theorem 1.1 in [8] we can finish the proof of Theorem 1.1. We omit the proof.…”

Iterated Commutators of Multilinear Maximal Square Functions on Some Function Spaces

“…Among these achievements, we mention the nice works of Bui and Duong [1], Grafakos, Liu and Yang [9], Maldonado and Naibo [14], Lu and Zhang [13], Tomita [23], Grafakos, Si [10] and more recent work of Grafakos, He and Honzík [8]. In 2017, Sun and Zhang [22] got the boundedness for commutators of multilinear Calderón-Zygmund operators with kernels of Dini type from product of Lebesgue spaces into Lebesgue spaces, Lipschitz spaces and homogenous Triebel-Lizorkin spaces, which extend some previous results. Very recently, the study for commutators of maximal operator of multilinear singular integral with kernels of Dini type was given by Si and Zhang [21].…”