Weighted $L^p$-boundedness of singular integrals with rough kernel associated to surfaces

다국어 초록 (Multilingual 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.

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