weighted L^p-boundedness of singular integrals with rough kernel associated to surfaces
J. Korean Math. Soc.
Published online May 26, 2020
Ronghui Liu and Huoxiong Wu
Xiamen University
Abstract : In this paper, we prove weighted norm inequalities for rough singular integrals along surfaces with radial kernels $h$ and sphere kernels $\Omega$ by assuming $h\in{\triangle}_{\gamma}(\mathbb{R}_+)$ and $\Omega\in\mathcal{WG}_\beta({\rm S}^{n-1})$ for some $\gamma>1$ and $\beta>1$. Here $\Omega\in\mathcal{WG}_\beta({\rm S}^{n-1})$ 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.
Keywords : Singular integrals, maximal operators, rough kernels, weighted norm inequalities.
MSC numbers : 42B20, 42B15, 42B25.
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