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Mat. Sb. (N.S.), 1984, Volume 123(165), Number 2, Pages 243–257 (Mi msb1996)  

This article is cited in 1 scientific paper (total in 1 paper)

On the vanishing of the symbol of a convolution integral operator

V. D. Stepanov


Abstract: The class $\operatorname{Int}(p,p)$ of kernels of convolution integral operators is defined, and a criterion for a measurable function to belong to $\operatorname{Int}(p,p)$ is given. The question of the behavior of the Fourier transform of a kernel (the symbol) in $\operatorname{Int}(2,2)$ is considered, and it is shown that in the sense of order the symbol can vanish at infinity in an arbitrarily slow manner, and more slowly than any power in the mean.
Bibliography: 6 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:1, 239–253

Bibliographic databases:

UDC: 517.444
MSC: 42A45, 42A85, 44A35
Received: 07.07.1983

Citation: V. D. Stepanov, “On the vanishing of the symbol of a convolution integral operator”, Mat. Sb. (N.S.), 123(165):2 (1984), 243–257; Math. USSR-Sb., 51:1 (1985), 239–253

Citation in format AMSBIB
\Bibitem{Ste84}
\by V.~D.~Stepanov
\paper On the vanishing of the symbol of a~convolution integral operator
\jour Mat. Sb. (N.S.)
\yr 1984
\vol 123(165)
\issue 2
\pages 243--257
\mathnet{http://mi.mathnet.ru/msb1996}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=732388}
\zmath{https://zbmath.org/?q=an:0568.45013|0543.45012}
\transl
\jour Math. USSR-Sb.
\yr 1985
\vol 51
\issue 1
\pages 239--253
\crossref{https://doi.org/10.1070/SM1985v051n01ABEH002857}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Stepanov V., “On Fourier Integral Multiplicators Generated by the Characteristic Set-Functions”, 299, no. 5, 1988, 1068–1070  mathscinet  zmath  isi
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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