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

Eurasian Mathematical Journal

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ЖУРНАЛЫ ПЕРСОНАЛИИ ОРГАНИЗАЦИИ КОНФЕРЕНЦИИ СЕМИНАРЫ ВИДЕОТЕКА ПАКЕТ AMSBIB

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Eurasian Mathematical Journal, 2010, том 1, номер 1, страницы 32–53 (Mi emj6)

Эта публикация цитируется в 29 научных статьях (всего в 29 статьях)

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

V. I. Burenkov^a, V. S. Guliyev^b, A. Serbetci^c, T. V. Tararykova^a

^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

PDF полного текста (377 kB) Список цитирования (29)

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Аннотация: 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.

Ключевые слова и фразы: singular integral operator, maximal operator, local Morrey-type spaces, Hardy operator on the cone of monotonic functions, weak Morrey-type spaces, weighted estimates.

Поступила в редакцию: 01.10.2009

Реферативные базы данных:

Тип публикации: Статья

MSC: 42B20, 42B25, 42B35

Язык публикации: английский

Образец цитирования: 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

Цитирование в формате AMSBIB

\RBibitem{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}

Образцы ссылок на эту страницу:

https://www.mathnet.ru/rus/emj6

https://www.mathnet.ru/rus/emj/v1/i1/p32

Эта публикация цитируется в следующих 29 статьяx:

Burenkov V.I. Chigambayeva D.K. Nursultanov E.D., “Marcinkiewicz-Type Interpolation Theorem For Morrey-Type Spaces and Its Corollaries”, Complex Var. Elliptic Equ., 65:1, SI (2020), 87–108
Guliyev V.S., Kucukaslan A., Aykol C., Serbetci A., “Riesz Potential in the Local Morrey-Lorentz Spaces and Some Applications”, Georgian Math. J., 27:4 (2020), 557–567
Farid G., Akbar S.B., Rehman Sh.U., Pecaric J., “Boundedness of Fractional Integral Operators Containing Mittag-Leffler Functions Via (S, M)-Convexity”, AIMS Math., 5:2 (2020), 966–978
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
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
Guliyev V.S. Hasanov S.G. Sawano Y., “Decompositions of Local Morrey-Type Spaces”, Positivity, 21:3 (2017), 1223–1252
Nakamura Sh., Sawano Y., “The Singular Integral Operator and Its Commutator on Weighted Morrey Spaces”, Collect. Math., 68:2 (2017), 145–174
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
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
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
В. И. Буренков, Т. В. Тарарыкова, “Аналог неравенства Юнга для сверток функций для общих пространств типа Морри”, Функциональные пространства, теория приближений, смежные разделы математического анализа, Сборник статей. К 110-летию со дня рождения академика Сергея Михайловича Никольского, Труды МИАН, 293, МАИК «Наука/Интерпериодика», М., 2016, 113–132 ; 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
Nakai E. Sobukawa T., “B-W(U)-Function Spaces and Their Interpolation”, Tokyo J. Math., 39:2 (2016), 483–516
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
Mustafayev R.Ch. Unver T., “Embeddings Between Weighted Local Morrey-Type Spaces and Weighted Lebesgue Spaces”, J. Math. Inequal., 9:1 (2015), 277–296
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
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
Sawano Y., Yabuta K., “Fractional Type Marcinkiewicz Integral Operators Associated to Surfaces”, J. Inequal. Appl., 2014, 232
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
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
R. M. Rzaev, “Properties of singular integrals in terms of maximal functions measuring smoothness”, Eurasian Math. J., 4:3 (2013), 107–119

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

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