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Mat. Sb., 1992, Volume 183, Number 9, Pages 89–104 (Mi msb1073)  

Calderón–Zygmund theory for kernels with nondiscrete sets of singularities

N. M. Kasumov


Abstract: An approach encompassing diverse locations of the singularities of convolution kernels by a single method is presented. In particular, the author introduces the notion of a so-called supersingular kernel, whose singularities lie on a set of arbitrary structure, in general, and a theorem on the continuity in $L^p(\mathbb R^N)$, $1<p<\infty$, of the operator of convolution with it is established. Together with the theorem on convergence almost everywhere of the sequence of convolutions defining this operator, with cutoffs of the kernel defined in a special way, it is a generalization of fundamental results of Calderón–Zygmund.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:1, 77–91

Bibliographic databases:

UDC: 517.98
MSC: 42B20
Received: 20.03.1991

Citation: N. M. Kasumov, “Calderón–Zygmund theory for kernels with nondiscrete sets of singularities”, Mat. Sb., 183:9 (1992), 89–104; Russian Acad. Sci. Sb. Math., 77:1 (1994), 77–91

Citation in format AMSBIB
\Bibitem{Kas92}
\by N.~M.~Kasumov
\paper Calder\'on--Zygmund theory for kernels with nondiscrete sets of singularities
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 9
\pages 89--104
\mathnet{http://mi.mathnet.ru/msb1073}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1198836}
\zmath{https://zbmath.org/?q=an:0789.42012|0772.42008}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 1
\pages 77--91
\crossref{https://doi.org/10.1070/SM1994v077n01ABEH003430}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994MZ10900006}


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