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Eurasian Mathematical Journal, 2010, Volume 1, Number 1, Pages 32–53 (Mi emj6)  
This article is cited in 29 scientific papers (total in 29 papers)

Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local Morrey-type spaces

V. I. Burenkova, V. S. Guliyevb, A. Serbetcic, T. V. Tararykovaa

a Faculty of Mathematics and Information Technology, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan
b Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku, Azerbaijan
c Ankara University, Department of Mathematics, Tandogan-Ankara, Turkey
Full-text PDF (377 kB) Citations (29)
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Abstract: The problem of the boundedness of a Calderon-Zygmund singular integral operator $T$ in local Morrey-type spaces is reduced to the boundedness of the Hardy operator in weighted $L_p$-spaces on the cone of non-negative non-increasing functions. This allows obtaining sufficient conditions for the boundedness of $T$ in local Morrey-type spaces for all admissible values of the parameters. Moreover, for a certain range of the parameters, for a genuine Calderon-Zygmund singular integral operator these sufficient conditions coincide with the necessary ones.
Keywords and phrases: singular integral operator, maximal operator, local Morrey-type spaces, Hardy operator on the cone of monotonic functions, weak Morrey-type spaces, weighted estimates.
Received: 01.10.2009
Bibliographic databases:
Document Type: Article
MSC: 42B20, 42B25, 42B35
Language: English
Citation: V. I. Burenkov, V. S. Guliyev, A. Serbetci, T. V. Tararykova, “Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local Morrey-type spaces”, Eurasian Math. J., 1:1 (2010), 32–53
Citation in format AMSBIB
\Bibitem{BurGulSer10}
\by V.~I.~Burenkov, V.~S.~Guliyev, A.~Serbetci, T.~V.~Tararykova
\paper Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local Morrey-type spaces
\jour Eurasian Math. J.
\yr 2010
\vol 1
\issue 1
\pages 32--53
\mathnet{http://mi.mathnet.ru/emj6}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2898674}
\zmath{https://zbmath.org/?q=an:1215.42019}
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    • This publication is cited in the following 29 articles:
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