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Izv. Akad. Nauk SSSR Ser. Mat., 1983, Volume 47, Issue 2, Pages 335–355 (Mi izv1394)  

A criterion for boundedness of singular integral operators with complicated singularities

A. G. Sergeev


Abstract: Singular integral operators acting on the space of (essentially) bounded functions defined on a smooth submanifold of $\mathbf R^n$ are considered. The singularities of the integrals given by the zeros of functions composing the integrand lie on smooth submanifolds. The basic result is as follows: if these submanifolds satisfy certain conditions of nondegeneracy type and the integral operator has no formal singularities (i.e., certain relations between the orders of the integrands and the dimensions of the manifolds of singularities are satisfied), then the singular integral operator is bounded on the space considered.
Bibliography: 4 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1984, 22:2, 309–327

Bibliographic databases:

Document Type: Article
UDC: 517.5
MSC: Primary 47G05; Secondary 05C99
Received: 25.05.1982

Citation: A. G. Sergeev, “A criterion for boundedness of singular integral operators with complicated singularities”, Izv. Akad. Nauk SSSR Ser. Mat., 47:2 (1983), 335–355; Math. USSR-Izv., 22:2 (1984), 309–327

Citation in format AMSBIB
\Bibitem{Ser83}
\by A.~G.~Sergeev
\paper A~criterion for boundedness of singular integral operators with complicated singularities
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1983
\vol 47
\issue 2
\pages 335--355
\mathnet{http://mi.mathnet.ru/izv1394}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=697299}
\zmath{https://zbmath.org/?q=an:0532.45009|0521.45010}
\transl
\jour Math. USSR-Izv.
\yr 1984
\vol 22
\issue 2
\pages 309--327
\crossref{https://doi.org/10.1070/IM1984v022n02ABEH001445}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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