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Eurasian Math. J., 2010, Volume 1, Number 1, Pages 32–53 (Mi emj6)  

This article is cited in 26 scientific papers (total in 26 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

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.

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MSC: 42B20, 42B25, 42B35
Received: 01.10.2009
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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://www.ams.org/mathscinet-getitem?mr=2898674}
\zmath{https://zbmath.org/?q=an:1215.42019}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. I. Burenkov, P. Jain, T. V. Tararykova, “On boundedness of the Hardy operator in Morrey-type spaces”, Eurasian Math. J., 2:1 (2011), 52–80  mathnet  mathscinet  zmath
    2. A. Akbulut, I. Ekincioglu, A. Serbetci, T. Tararykova, “Boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces”, Eurasian Math. J., 2:2 (2011), 5–30  mathnet  mathscinet  zmath
    3. Guliyev V.S., Aliyev S.S., Karaman T., “Boundedness of a Class of Sublinear Operators and Their Commutators on Generalized Morrey Spaces”, Abstr. Appl. Anal., 2011, 356041, 18 pp.  mathscinet  zmath  isi  elib
    4. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. I”, Eurasian Math. J., 3:3 (2012), 11–32  mathnet  mathscinet  zmath
    5. V. S. Guliyev, “Generalized weighted Morrey spaces and higher order commutators of sublinear operators”, Eurasian Math. J., 3:3 (2012), 33–61  mathnet  mathscinet  zmath
    6. Fan Yu., Gao G., “Some Estimates of Rough Bilinear Fractional Integral”, J. Funct. Space Appl., 2012, 406540  crossref  mathscinet  zmath  isi  elib
    7. Akbulut A., Guliyev V.S., Muradova Sh.A., “Boundedness of the Anisotropic Riesz Potential in Anisotropic Local Morrey-Type Spaces”, Complex Var. Elliptic Equ., 58:2 (2013), 259–280  crossref  mathscinet  zmath  isi  elib
    8. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Math. J., 4:1 (2013), 21–45  mathnet  mathscinet  zmath
    9. R. M. Rzaev, “Properties of singular integrals in terms of maximal functions measuring smoothness”, Eurasian Math. J., 4:3 (2013), 107–119  mathnet
    10. Fan Yu., “Boundedness of Sublinear Operators and Their Commutators on Generalized Central Morrey Spaces”, J. Inequal. Appl., 2013, 411  crossref  mathscinet  isi  scopus
    11. Aykol C., Guliyev V.S., Serbetci A., “Boundedness of the Maximal Operator in the Local Morrey-Lorentz Spaces”, J. Inequal. Appl., 2013, 346  crossref  mathscinet  zmath  isi  scopus
    12. Burenkov V.I. Oinarov R., “Necessary and Sufficient Conditions For Boundedness of the Hardy-Type Operator From a Weighted Lebesgue Space to a Morrey-Type Space”, Math. Inequal. Appl., 16:1 (2013), 1–19  crossref  mathscinet  zmath  isi  scopus
    13. Sawano Y., Yabuta K., “Fractional Type Marcinkiewicz Integral Operators Associated to Surfaces”, J. Inequal. Appl., 2014, 232  crossref  mathscinet  zmath  isi
    14. Mustafayev R.Ch. Unver T., “Embeddings Between Weighted Local Morrey-Type Spaces and Weighted Lebesgue Spaces”, J. Math. Inequal., 9:1 (2015), 277–296  crossref  mathscinet  zmath  isi  elib
    15. Balakishiyev A.S., Guliyev V.S., Gurbuz F., Serbetci A., “Sublinear Operators With Rough Kernel Generated By Calderon-Zygmund Operators and Their Commutators on Generalized Local Morrey Spaces”, J. Inequal. Appl., 2015, 61  crossref  mathscinet  zmath  isi  elib
    16. Izuki M., Nakai E., Sawano Y., “Wavelet Characterization and Modular Inequalities For Weighted Lebesgue Spaces With Variable Exponent”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 40:2 (2015), 551–571  crossref  mathscinet  zmath  isi
    17. Long P., Han H., “Characterizations of Some Operators on the Vanishing Generalized Morrey Spaces With Variable Exponent”, J. Math. Anal. Appl., 437:1 (2016), 419–430  crossref  mathscinet  zmath  isi  elib
    18. Hakim D.I., Nakai E., Sawano Y., “Generalized Fractional Maximal Operators and Vector-Valued Inequalities on Generalized Orlicz-Morrey Spaces”, Rev. Mat. Complut., 29:1 (2016), 59–90  crossref  mathscinet  zmath  isi  elib
    19. V. I. Burenkov, T. V. Tararykova, “An analog of Young's inequality for convolutions of functions for general Morrey-type spaces”, Proc. Steklov Inst. Math., 293 (2016), 107–126  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    20. Nakai E. Sobukawa T., “B-W(U)-Function Spaces and Their Interpolation”, Tokyo J. Math., 39:2 (2016), 483–516  crossref  mathscinet  zmath  isi  scopus
    21. Guliyev V.S., Aykol C., Kucukaslan A., Serbetci A., “Maximal Operator and Calderon-Zygmund Operators in Local Morrey-Lorentz Spaces”, Integral Transform. Spec. Funct., 27:11 (2016), 866–877  crossref  mathscinet  zmath  isi  scopus
    22. A. Gogatishvili, R. Mustafayev, T. Ünver, “Embedding relations between weighted complementary local Morrey-type spaces and weighted local Morrey-type spaces”, Eurasian Math. J., 8:1 (2017), 34–49  mathnet
    23. Guliyev V.S. Hasanov S.G. Sawano Y., “Decompositions of Local Morrey-Type Spaces”, Positivity, 21:3 (2017), 1223–1252  crossref  isi
    24. Nakamura Sh., Sawano Y., “The Singular Integral Operator and Its Commutator on Weighted Morrey Spaces”, Collect. Math., 68:2 (2017), 145–174  crossref  isi
    25. Guliyev V.S., Koca K., Mustafayev R.C.H., Unver T., “Boundedness of Operators Arising From Schwarz Bvp in Modified Local Morrey-Type Spaces”, Complex Var. Elliptic Equ., 62:10, SI (2017), 1541–1557  crossref  isi
    26. Sawano Y. Yoshida H., “A Predual of a Predual of B (SIGMA) and Its Applications to Commutators”, Sci. China-Math., 61:8 (2018), 1437–1472  crossref  mathscinet  zmath  isi  scopus
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