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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 4, Pages 676–704 (Mi izv1486)  

On integrability of the Banach indicatrix of a smooth mapping

S. A. Gulevich


Abstract: Let $f\colon\mathbf R^n\to\mathbf R^n$ be a mapping of class $C^{(l)}$ with compact support, and let $N(f,y)$ be the number of solutions of the equation $f(x)=y$. It is proved that if $p<l$, then $\int[N(f,y)]^p dy<\infty$, and an example is given which shows that this integral can diverge if $p>l$.
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:1, 19–44

Bibliographic databases:

UDC: 517.98
MSC: 58C25
Received: 15.02.1984

Citation: S. A. Gulevich, “On integrability of the Banach indicatrix of a smooth mapping”, Izv. Akad. Nauk SSSR Ser. Mat., 48:4 (1984), 676–704; Math. USSR-Izv., 25:1 (1985), 19–44

Citation in format AMSBIB
\Bibitem{Gul84}
\by S.~A.~Gulevich
\paper On~integrability of the Banach indicatrix of a~smooth mapping
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 4
\pages 676--704
\mathnet{http://mi.mathnet.ru/izv1486}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=755953}
\zmath{https://zbmath.org/?q=an:0581.58004}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 1
\pages 19--44
\crossref{https://doi.org/10.1070/IM1985v025n01ABEH001263}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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