The necessity theory for commutators of multilinear singular integral operators: the weighted case

2021/04/11 by Dinghuai Wang, Wang, Dinghuai
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2104.04967

openalex publication_date 2021/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the necessity theory for commutators of multilinear singular integral operators on weighted Lebesgue spaces is investigated. The results relax the restriction of the weights class to the general multiple weights, which can be regarded as an essential improvement of \citeChafCruz2018,GLW2020. Our approach elaborates on a commonly expanding the kernel locally by Fourier series, recovering many known results but yielding also numerous new ones. In particular, we answer the question about the necessity theory of the iterated commutators of the multilinear singular integral operators.

Citations

• On functions of bounded mean oscillation
• Multilinear Calderón–Zygmund Theory
• On commutators of singular integrals and bilinear singular integrals
• Hp spaces of several variables
• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

Related

• Multiple Weighted Estimates for Multilinear Commutators of Multilinear Singular Integrals with Generalized Kernels
• Weighted vector-valued bounds for a class of multilinear singular integral operators
• Compactness of commutators of multilinear singular integral operators with non-smooth kernels
• Weighted Estimates for the iterated Commutators of Multilinear Maximal and Fractional Type Operators
• Some extensions of classes involving pair of weights related to the boundedness of multilinear commutators associated to generalized fractional integral operators