Abstract
Motivated by the composition of singular integral operators, we introduce a class of singular integral operators in the Euclidean space \(\mathbb {R}^{n}\) with kernels supported in surfaces in \( \mathbb {R}^{n}\times \mathbb {R}^{n}\). The surfaces are allowed to be very flat at the origin in \(\mathbb {R}^{n}\times \mathbb {R}^{n}\). The boundedness of the operators on \(L^{p}\) is proved under the assumption that the kernels are rough in \(L(\log L)^{2}(\mathbb {S}^{n-1}\times \mathbb {S}^{n-1})\).
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Al-Salman, A. Singular Integral Operators Supported in Higher Dimensional Surfaces. Mediterr. J. Math. 20, 275 (2023). https://doi.org/10.1007/s00009-023-02476-1
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DOI: https://doi.org/10.1007/s00009-023-02476-1
Keywords
- Singular integral operators
- rough kernels
- \(L^{p}\) estimates
- singular Radon transforms
- Fourier transform
- maximal functions