Weak and strong type estimates for the multilinear Littlewood-Paley operators

2020/09/29 by Mingming Cao, Cao, Mingming, Mahdi Hormozi +9
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2009.13814

openalex publication_date 2020/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S_α be the multilinear square function defined on the cone with aperture α≥ 1. In this paper, we investigate several kinds of weighted norm inequalities for S_α. We first obtain a sharp weighted estimate in terms of aperture α and w ∈ A_p. By means of some pointwise estimates, we also establish two-weight inequalities including bump and entropy bump estimates, and Fefferman-Stein inequalities with arbitrary weights. Beyond that, we consider the mixed weak type estimates corresponding Sawyer's conjecture, for which a Coifman-Fefferman inequality with the precise A_∞ norm is proved. Finally, we present the local decay estimates using the extrapolation techniques and dyadic analysis respectively. All the conclusions aforementioned hold for the Littlewood-Paley g^*_λ function. Some results are new even in the linear case.

Citations

• New maximal functions and multiple weights for the multilinear Calderón–Zygmund theory

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