Weighted estimates for maximal bilinear rough singular integrals via sparse dominations

• Wang, Zhidan ^[1] ; Xue, Qingying ^[1] ; Duan, Xinchen ^[1]
  1. [1] Beijing Normal University

     Beijing Normal University

     China

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 73, Fasc. 1, 2022, págs. 55-73
• Idioma: inglés
• DOI: 10.1007/s13348-020-00307-0
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let x=(x1,x2) with x1,x2∈Rn and let K(x)=Ω(x/|x|)∣∣x∣∣−2n, where Ω∈L∞(S2n−1) and satisfies ∫S2n−1Ω=0. We show that the maximal truncated bilinear singular integrals with rough kernel K(x1,x2) satisfy a sparse bound by (p, p, p)-averages for all p>1. As consequences, we obtain some quantitative weighted estimates for these rough singular integrals. A pointwise sparse domination for commutators of bilinear rough singular integrals were also established, which can be used to establish some weighted inqualities.