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http://dx.doi.org/10.4134/JKMS.j190845

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)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.1, 2021 , pp. 69-90 More about this Journal
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
Singular integrals; maximal operators; rough kernels; weighted norm inequalities;
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