Sharp bilinear estimates for maximal singular integrals with kernels in weighted L^q spaces

2025/10/22 by Stefanos Lappas, Bae Jun Park, Lappas, Stefanos +1
Mathematics · #42B20 #42B25 #47H60 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2510.19184

openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the boundedness properties of the (dyadic) maximal bilinear operator associated with rough homogeneous kernels on ℝ. We establish sharp L^p₁(ℝ) × L^p₂(ℝ) → L^p(ℝ) estimates in the full quasi-Banach range of exponents 1 < p₁, p₂ < ∞ and 1/2 < p < ∞. Our approach extends and unifies several recent contributions, including those of Honzík, the first author, and Slavíkova, as well as the second author in the bilinear and in the one-dimensional settings, by allowing the angular component Ω of the kernel to belong to weighted L^q-spaces on \mathbbS¹.

Citations

• An alternate approach to bilinear rough singular integrals
• Bilinear singular integral operators with kernels in weighted spaces
• Multilinear estimates for maximal rough singular integrals
• Bilinear Rough Singular Integrals near the Critical Integrability via Sharp Fourier Multiplier Criteria
• Multilinear singular integrals with homogeneous kernels near L¹
• Multilinear rough singular integral operators
• The full range of uniform bounds for the bilinear Hilbert transform
• Improved estimates for bilinear rough singular integrals
• On pointwise a.e. convergence of multilinear operators
• Rough Bilinear Singular Integrals
• On commutators of singular integrals and bilinear singular integrals
• On the existence of certain singular integrals

Related

• Bilinear singular integral operators with kernels in weighted spaces
• An alternate approach to bilinear rough singular integrals
• A bilinear sparse domination for the maximal singular integral operators with rough kernels
• Quantitative weighted estimates for rough homogeneous singular integrals
• Weighted Estimates for Rough Bilinear Singular Integrals via Sparse Domination