Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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WEIGHTED Lp-BOUNDEDNESS OF SINGULAR INTEGRALS WITH ROUGH KERNEL ASSOCIATED TO SURFACES

  • Liu, Ronghui (School of Mathematical Sciences Xiamen University) ;
  • Wu, Huoxiong (School of Mathematical Sciences Xiamen University)
  • Received : 2019.12.17
  • Accepted : 2020.03.19
  • Published : 2021.01.01
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Abstract

In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels h and sphere kernels Ω by assuming h ∈ △γ(ℝ+) and Ω ∈ ����β(Sn-1) for some γ > 1 and β > 1. Here Ω ∈ ����β(Sn-1) denotes the variant of Grafakos-Stefanov type size conditions on the unit sphere. Our results essentially improve and extend the previous weighted results for the rough singular integrals and the corresponding maximal truncated operators.

Keywords

Acknowledgement

The research was supported by NNSF of China (Nos. 11771358, 11871101).

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