Commutators of parametric Marcinkiewicz integrals on generalized Orlicz-Morrey spaces

Year 2017, Volume: 66 Issue: 1, 115 - 123, 01.02.2017

Fatih Derıngoz

https://doi.org/10.1501/Commua1_0000000781

Cited By: 2

Abstract

In this paper, we study the boundedness of the commutators ofparametric Marcinkiewicz integral operator with smooth kernel on generalized Orlicz-Morrey spaces

Keywords

Parametric Marcinkiewicz integrals, generalized Orlicz-Morrey spaces, commutator, BM O

References

• Aliyev, S. S. and Guliyev, V. S., Boundedness of parametric Marcinkiewicz integral operator and their commutators on generalized Morrey spaces, Georgian Math. J. (2012), 19, 195-208. [2] Deringoz, F., Guliyev, V. S. and Samko, S., Boundedness of maximal and singular operators on generalized Orlicz-Morrey spaces, Operator Theory, Operator Algebras and Applications, Series: Operator Theory: Advances and Applications 242, 139-158, 2014.
• Deringoz, F., Guliyev, V. S. and Samko, S., Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces, Ann. Acad. Sci. Fenn. Math. (2015), 40, 535-549.
• Cui, R. and Li, Z., Boundedness of Marcinkiewicz integrals and their commutators on gener- alized weighted Morrey spaces, J. Funct. Spaces (2015), Art. ID 450145, 9 pp.
• Fu, X., Yang, D. and Yuan, W., Boundedness of multilinear commutators of Calderón- Zygmund operators on Orlicz spaces over non-homogeneous spaces, Taiwanese J. Math. (2012), 16, 2203-2238.
• Gala, S., Sawano, Y. and Tanaka, H., A remark on two generalized Orlicz-Morrey spaces, J. Approx. Theory (2015), 98, 1-9.
• Guliyev, V. S., Generalized local Morrey spaces and fractional integral operators with rough kernel, J. Math. Sci. (N. Y.) (2013), 193(2), 211-227.
• Guliyev, V. S. and Deringoz, F., On the Riesz potential and its commutators on generalized Orlicz-Morrey spaces, J. Funct. Spaces (2014), Article ID 617414, 11 pages.
• Guliyev, V. S., Deringoz, F. and Hasanov, J. J.
• admissible singular operators and their commutators on vanishing generalized Orlicz-Morrey spaces, J. Inequal. Appl. (2014), 2014:143, 18 pp.
• Guliyev, V. S., Hasanov, S. G., Sawano, Y. and Noi, T., Non-smooth Atomic Decompositions for Generalized Orlicz-Morrey Spaces of the Third Kind, Acta Appl. Math. (2016), DOI 10.1007/s10440-016-0052-7.
• Ho, Kwok-Pun, Characterization of BMO in terms of rearrangement-invariant Banach func- tion spaces, Expo. Math. (2009), 27, 363-372
• Hörmander, L., Translation invariant operators, Acta Math. (1960), 104, 93-139.
• Janson, S., Mean oscillation and commutators of singular integral operators, Ark. Mat. (1978), 16, 263-270 .
• Nakai, E., Generalized fractional integrals on Orlicz-Morrey spaces. In: Banach and Function Spaces, (Kitakyushu, 2003), Yokohama Publishers, Yokohama, 323-333, 2004.
• Sawano, Y., Sugano, S. and Tanaka, H., Orlicz-Morrey spaces and fractional operators, Po- tential Anal. (2012), 36(4), 517-556.
• Shi, X. and Jiang, Y., Weighted boundedness of parametric Marcinkiewicz integral and higher order commutator, Anal. Theory Appl. (2009), 25(1), 25-39.
• Stein, E. M., On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz, Trans. Amer. Math. Soc. (1958), 88, 430-466.