Rough singular integrals associated to surfaces of revolution

Lu, Shanzhen; Pan, Yibiao; Yang, Dachun

doi:10.1090/S0002-9939-01-05893-2

Rough singular integrals associated to surfaces of revolution
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by Shanzhen Lu, Yibiao Pan and Dachun Yang PDF

Proc. Amer. Math. Soc. 129 (2001), 2931-2940 Request permission

Abstract:

Let $1<p<\infty$ and $n\ge 2$. The authors establish the $L^p(\mathbb {R}^{n+1})$-boundedness for a class of singular integral operators associated to surfaces of revolution, $\{(t,\phi (|t|)):\ t\in \mathbb {R}^n\}$, with rough kernels, provided that the corresponding maximal function along the plane curve $\{(t, \phi (|t|)):\ t\in \mathbb {R}\}$ is bounded on $L^p(\mathbb {R}^2)$.

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