RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Eurasian Math. J.: Year: Volume: Issue: Page: Find

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

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.

Full text: PDF file (377 kB)
References: PDF file   HTML file

Bibliographic databases:

MSC: 42B20, 42B25, 42B35
Language:

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} 

• http://mi.mathnet.ru/eng/emj6
• http://mi.mathnet.ru/eng/emj/v1/i1/p32

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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
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
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.
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
5. V. S. Guliyev, “Generalized weighted Morrey spaces and higher order commutators of sublinear operators”, Eurasian Math. J., 3:3 (2012), 33–61
6. Fan Yu., Gao G., “Some Estimates of Rough Bilinear Fractional Integral”, J. Funct. Space Appl., 2012, 406540
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
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
9. R. M. Rzaev, “Properties of singular integrals in terms of maximal functions measuring smoothness”, Eurasian Math. J., 4:3 (2013), 107–119
10. Fan Yu., “Boundedness of Sublinear Operators and Their Commutators on Generalized Central Morrey Spaces”, J. Inequal. Appl., 2013, 411
11. Aykol C., Guliyev V.S., Serbetci A., “Boundedness of the Maximal Operator in the Local Morrey-Lorentz Spaces”, J. Inequal. Appl., 2013, 346
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
13. Sawano Y., Yabuta K., “Fractional Type Marcinkiewicz Integral Operators Associated to Surfaces”, J. Inequal. Appl., 2014, 232
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
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
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
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
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
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
20. Nakai E. Sobukawa T., “B-W(U)-Function Spaces and Their Interpolation”, Tokyo J. Math., 39:2 (2016), 483–516
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
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
23. Guliyev V.S. Hasanov S.G. Sawano Y., “Decompositions of Local Morrey-Type Spaces”, Positivity, 21:3 (2017), 1223–1252
24. Nakamura Sh., Sawano Y., “The Singular Integral Operator and Its Commutator on Weighted Morrey Spaces”, Collect. Math., 68:2 (2017), 145–174
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
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
•  Number of views: This page: 627 Full text: 346 References: 236