Hostname: page-component-76fb5796d-zzh7m Total loading time: 0 Render date: 2024-04-26T15:31:13.797Z Has data issue: false hasContentIssue false

Some Estimates for Generalized Commutators of Rough Fractional Maximal and Integral Operators on Generalized Weighted Morrey Spaces

Published online by Cambridge University Press:  20 November 2018

Ferit Gürbüz*
Affiliation:
Ankara University, Faculty of Science, Department of Mathematics, Tandoğan 06100, Ankara, Turkey e-mail: feritgurbuz84@hotmail.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we establish $BMO$ estimates for generalized commutators of rough fractional maximal and integral operators on generalized weighted Morrey spaces, respectively.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2017

References

[1] Akbulut, A., Hamzayev, V. H., and Safarov, Z. V., Boundedness of rough fractional multilinear integral operators on generalized Morrey spaces. J. Inequal. Appl. 234(2015). http://dx.doi.Org/10.1186/s13660-015-0751-z Google Scholar
[2] Chiarenza, F. and Frasca, M., Morrey spaces and Hardy-Littlewood maximal function. Rend. Mat. Appl. 7(1987), 273279.Google Scholar
[3] Cohen, J. and Gosselin, J., A BMO estimate for multilinear singular integrals. Illinois J. Math. 30(1986), 445464.Google Scholar
[4] Ding, Y., Weak type bounds for a class of rough operators with power weights. Proc. Amer. Math. Soc. 125(1997), 29392942. http://dx.doi.Org/10.1090/S0002-9939-97-03914-2 Google Scholar
[5] Ding, Y. and Lu, S. Z., Weighted norm inequalities for fractional integral operators with rough kernel. Canad. J. Math. 50(1998), 2939. http://dx.doi.Org/10.4153/CJM-1998-003-1 Google Scholar
[6] Di Fazio, G. and Ragusa, M. A., Interior estimates in Morrey spaces for strong solutions to nondivergence form equations with discontinuous coefficients. J. Funct. Anal. 112(1993), 241256. http://dx.doi.Org/10.1006/jfan.1993.1032 Google Scholar
[7] Garcia-Cuerva, J. and Rubio de Francia, J. L., Weighted norm inequalities and related topics. North-Holland Mathematics Studies, 116, North-Holland Publishing, Amsterdam, 1985.Google Scholar
[8] Guliyev, V. S., Generalized weighted Morrey spaces and higher order commutators ofsublinear operators. Eurasian Math. J. 3(2012), no. 3, 3361.Google Scholar
[9] John, F. and Nirenberg, L., On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14(1961), 415426. http://dx.doi.Org/10.1002/cpa.3160140317 Google Scholar
[10] Karaman, T., Boundedness of some classes ofsublinear operators on generalized weighted Morrey spaces and some applications. (Turkish) Ph.D. thesis, Ankara University, Ankara, Turkey, 2012.Google Scholar
[11] Komori, Y. and Shirai, S., Weighted Morrey spaces and a singular integral operator. Math. Nachr. 282(2009), 219231. http://dx.doi.Org/10.1 OO2/mana.2OO610733 Google Scholar
[12] Lin, Y. and Lu, S. Z., Strongly singular Calderdn-Zygmund operators and their commutators. Jordan J. Math. Stat. (JJMS) 1(2008), 3149.Google Scholar
[13] Mizuhara, T., Boundedness of some classical operators on generalized Morrey spaces. In: Harmonic analysis, ICM-90 Satell. Conf. Proc, Springer, Tokyo, 1990, pp. 183189.Google Scholar
[14] Morrey, C. B., On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 43(1938), 126166. http://dx.doi.Org/10.1090/S0002-9947-1938-1501936-8 Google Scholar
[15] Muckenhoupt, B. and Wheeden, R. L., Weighted norm inequalities for singular and fractional integrals. Trans. Amer. Math. Soc. 161(1971), 249258. http://dx.doi.Org/10.1090/S0002-9947-1971-0285938-7 Google Scholar
[16] Palagachev, D. K. and Softova, L. G., Singular integral operators, Morrey spaces and fine regularity of solutions to PDE's. Potential Anal. 20(2004), 237263. http://dx.doi.Org/1 0.1023/B:POTA.0000010664.71 807.f6 Google Scholar
[17] Ragusa, M. A., Regularity of solutions of divergence form elliptic equation. Proc. Amer. Math. Soc. 128(2000), 533540. http://dx.doi.Org/10.1090/S0002-9939-99-05165-5 Google Scholar
[18] Wheeden, R. L. and Zygmund, A., Measure and integral: an introduction to real analysis. Pure and Applied Mathematics, 43, Marcel Dekker, New York, 1977.Google Scholar
[19] Wu, Q. and Yang, D. C., On fractional multilinear singular integrals. Math. Nachr. 239/240(2002), 215-235. http://dx.doi.Org/!0.1002/1522-2616(200206)239:1<21 5::AID-MANA21 5>3.0.CO;2-* 3.0.CO;2-*>Google Scholar