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Matematicheskie Zametki, 2022, Volume 111, Issue 3, Pages 422–432
DOI: https://doi.org/10.4213/mzm13078 (Mi mzm13078) 		 
On the Marcinkiewicz–Calderón Interpolation Theorem for Integral Operators

E. D. Nursultanovab, N. T. Tleukhanovac, Z. M. Mukeyevac

a Kazakhstan Branch of Lomonosov Moscow State University, Nur-Sultan
b Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan
c Eurasian National University named after L.N. Gumilyov, Nur-Sultan
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DOI: https://doi.org/10.4213/mzm13078
Abstract: The inverse problem to the classical Marcinkiewicz–Calderón interpolation theorem is considered. Necessary conditions for the Marcinkiewicz–Calderón theorem to hold for the integral operator under consideration are obtained in terms of the kernel of this operator. It is shown that these conditions are sufficient for the given integral operator to be of $(p,q)$-strong type for the same parameters $p$ and $q$ that appear in the interpolation theorem.
Keywords: integral operators, Marcinkiewicz interpolation theorem.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP08956157
This work was supported by the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AP08956157).
Received: 20.03.2021
Revised: 01.10.2021
English version:
Mathematical Notes, 2022, Volume 111, Issue 3, Pages 423–432
DOI: https://doi.org/10.1134/S0001434622030105
Bibliographic databases:
Document Type: Article
UDC: 517.5
PACS: 02.30.Tb , 02.30.Uu
Language: Russian
Citation: E. D. Nursultanov, N. T. Tleukhanova, Z. M. Mukeyeva, “On the Marcinkiewicz–Calderón Interpolation Theorem for Integral Operators”, Mat. Zametki, 111:3 (2022), 422–432; Math. Notes, 111:3 (2022), 423–432
Citation in format AMSBIB
\Bibitem{NurTleMuk22}
\by E.~D.~Nursultanov, N.~T.~Tleukhanova, Z.~M.~Mukeyeva
\paper On the Marcinkiewicz--Calder\'on Interpolation Theorem for Integral Operators
\jour Mat. Zametki
\yr 2022
\vol 111
\issue 3
\pages 422--432
\mathnet{http://mi.mathnet.ru/mzm13078}
\crossref{https://doi.org/10.4213/mzm13078}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4461272}
\transl
\jour Math. Notes
\yr 2022
\vol 111
\issue 3
\pages 423--432
\crossref{https://doi.org/10.1134/S0001434622030105}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85128980283}
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