Improved estimates for bilinear rough singular integrals

2021/04/29 by Danqing He, Bae Jun Park, He, Danqing +1 · 4 citations
Mathematics · #42B20 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2104.14137

openalex publication_date 2021/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study bilinear rough singular integral operators L_Ω associated with a function Ω on the sphere \mathbbS^2n-1. In the recent work of Grafakos, He, and Slavíková (Math. Ann. 376: 431-455, 2020), they showed that L_Ω is bounded from L²× L² to L¹, provided that Ω∈ L^q(\mathbbS^2n-1) for 4/3

Citations

• On functions of bounded mean oscillation
• Multilinear Calderón–Zygmund Theory
• On commutators of singular integrals and bilinear singular integrals
• Orthonormal bases of compactly supported wavelets

Cited by

• The Interplay of Shifted Square and Maximal Function Estimates in the Context of Multilinear Fourier Multipliers
• Sharp bilinear estimates for maximal singular integrals with kernels in weighted L^q spaces
• An alternate approach to bilinear rough singular integrals
• Sparse domination for rough multilinear singular integrals

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• Sparse domination and weighted estimates for rough bilinear singular integrals
• Multilinear rough singular integral operators
• Limiting weak-type behaviors for singular integrals with rough Llog L(\mathbbSⁿ) kernels