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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2001, Volume 232, Pages 164–178 (Mi tm211)  

Boundedness and Compactness Criteria for a Generalized Truncated Potential

V. M. Kokilashvili

A. Razmadze Mathematical Institute, Georgian Academy of Sciences
References:
Abstract: Boundedness and compactness criteria are established for a generalized truncated Riesz potential Kαf(x,t)=|y|2|x|(|xy|+t)αnf(y)dy, t[0,), xRn, that acts from Lp(Rn) to Lqν(Rn+1+), where 1<p<, 0<q<, α>n/p, and ν is a positive Borel measure on Rn+1+. Also, two-sided estimates for a measure of noncompactness of the operator Kα are obtained.
Received in July 2000
Bibliographic databases:
UDC: 517.444
Language: Russian
Citation: V. M. Kokilashvili, “Boundedness and Compactness Criteria for a Generalized Truncated Potential”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 232, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 164–178; Proc. Steklov Inst. Math., 232 (2001), 157–171
Citation in format AMSBIB
\Bibitem{Kok01}
\by V.~M.~Kokilashvili
\paper Boundedness and Compactness Criteria for a~Generalized Truncated Potential
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 164--178
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm211}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1851447}
\zmath{https://zbmath.org/?q=an:1006.47023}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 157--171
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    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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