Sparse domination for rough multilinear singular integrals

2025/06/22 by Dan, Binwei, Xue, Qingying
#42B20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.17905

Abstract

Let Ω be a function on ℝ^mn , homogeneous of degree zero, and satisfy a cancellation condition on the unit sphere \mathbbS^mn-1. In this paper, we show that the multilinear singular integral operator T_Ω(f₁, …, f_m)(x) := p.v. ∫_ℝ^mn \fracΩ(x - y₁, …, x - y_m)|x - y|^mn ∏_i=1^m f_i(y_i) dy, associated with a rough kernel Ω∈ L^r(\mathbbS^mn-1) , r > 1 , admits a sparse domination, where y=(y₁,…,y_m) and dy=dy₁⋯ dy_m. As a consequence, we derive some quantitative weighted norm inequalities for T_Ω .

Related

• Weighted estimates for Multilinear Singular Integrals with Rough Kernels
• A bilinear sparse domination for the maximal singular integral operators with rough kernels
• Sparse domination and weighted estimates for rough bilinear singular integrals
• Sparse bounds for maximal rough singular integrals via the Fourier transform
• A sparse domination for the Marcinkiewicz integral with rough kernel and applications