曲面上粗糙核奇异积分的加权L - p有界性

Pub Date : 2021-01-01 DOI:10.4134/JKMS.J190845

Ronghui Liu, Huo-xiong Wu

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引用次数: 0

摘要

。本文通过假设h∈(cid:52) γ (R +)和Ω∈WG β (S n−1)对于某些γ > 1和β > 1，证明了沿径向核为h和球核为Ω的粗糙奇异积分的加权范数不等式。其中Ω∈WG β (S n−1)表示单位球上的Grafakos-Stefanov型尺寸条件的变体。我们的结果从本质上改进和推广了粗糙奇异积分和相应的极大截断算子的加权结果。

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WEIGHTED L p -BOUNDEDNESS OF SINGULAR INTEGRALS WITH ROUGH KERNEL ASSOCIATED TO SURFACES

. 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 ∈ (cid:52) γ ( R + ) and Ω ∈ WG β (S n − 1 ) for some γ > 1 and β > 1. Here Ω ∈ WG β (S n − 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.

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