Boundedness of singular integrals along surfaces on Lebesgue spaces. (English) Zbl 1240.42089
Summary: We establish the \(L^p(\mathbb R^{n+1})\)-boundedness for a class of singular integral operators associated to surfaces of revolution \(\{(y, \gamma(|y|), y\in \mathbb R^n\}\) with rough kernels. We also give several applications of this inequality.
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B25 | Maximal functions, Littlewood-Paley theory |
Keywords:
singular integrals; surfaces; rough kernels; Plancherel’s theorem; oscillatory singular integralsReferences:
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