Improved estimates for bilinear rough singular integrals

@article{He2022ImprovedEF,
  title={Improved estimates for bilinear rough singular integrals},
  author={Danqing He and Bae Jun Park},
  journal={Mathematische Annalen},
  year={2022}
}
. We study bilinear rough singular integral operators L Ω associated with a function Ω on the sphere S 2 n − 1 . In the recent work of Grafakos, He, and Slav´ıkov´a [16], they showed that L Ω is bounded from L 2 × L 2 to L 1 , provided that Ω ∈ L q ( S 2 n − 1 ) for 4 / 3 < q ≤ ∞ with mean value zero. In this paper, we provide a generalization of their result. We actually prove L p 1 × L p 2 → L p estimates for L Ω under the assumption where 1 < p 1 , p 2 ≤ ∞ and 1 / 2 < p < ∞ with 1 /p = 1 /p… 

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