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Some characterizations of the generalized BMO spaces via the boundedness of maximal function commutators

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Abstract

In this paper, we investigated the commutators of Hardy–Littlewood maximal function with symbol function b in generalized BMO spaces. Some characterizations of generalized BMO spaces are obtained via the strong and weak boundedness of the commutators on Orlicz–Morrey space.

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References

  1. Agcayazi, M., Gogatishvili, A., Koca, K., Mustafayev, R.: A note on maximal commutators and commutators of maximal functions. J. Math. Soc. Jpn. 67(2), 581–593 (2015)

    Article  MathSciNet  Google Scholar 

  2. Bastero, J., Milman, M., Ruiz, F.J.: Commutators of the maximal and sharp functions. Proc. Am. Math. Soc. 128(11), 3329–3334 (2000)

    Article  MathSciNet  Google Scholar 

  3. Coifman, R.R., Rochberg, R., Weiss, G.: Factorization theorems for Hardy spaces in several variable. Ann. Math. 103(3), 611–635 (1976)

    Article  MathSciNet  Google Scholar 

  4. Deringoz, F., Guliyev, V.S., Hasanov, S.G.: Characterizations for the Riesz potential and its commutators on generalized Orlicz–Morrey spaces. J. Inequal. Appl. (2016). https://doi.org/10.1186/s13660-016-1192-z

    Article  MathSciNet  MATH  Google Scholar 

  5. Deringoz, F., Guliyev, V.S., Samko, S.: Boundedness of maximal and singular operators on generalized Orlicz–Morrey spaces. Theory Oper. Algebras Appl. Ser. Oper. Theory Adv. Appl. 242, 139–158 (2014)

    MathSciNet  MATH  Google Scholar 

  6. Fan, Y.: Some estimates of the commutator operators and the multilinear operators. Doctoral thesis (2012)

  7. Gogatishvili, A., Mustafayev, R., Agcayazi, M.: Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function. Tokyo J. Math. 41(1), 193–218 (2018)

    MathSciNet  MATH  Google Scholar 

  8. Guliyev, V.S., Deringoz, F.: On the Riesz potential and its commutators on generalized Orlicz–Morrey spaces. J. Funct. Spaces (2014). Article ID 617414. https://doi.org/10.1155/2014/617414

  9. Guliyev, V.S., Deringoz, F.: Some characterizations of Lipschitz spaces via commutators on generalized Orlicz–Morrey spaces. Mediterr. J. Math. 15(4), 180 (2018). https://doi.org/10.1007/s00009-018-1226-5

    Article  MathSciNet  MATH  Google Scholar 

  10. Guliyev, V.S., Deringoz, F., Hasanov, S.G.: Riesz potential and its commutators on Orlicz spaces. J. Inequal. Appl. Paper No. 75, 18 pp (2017). https://doi.org/10.1186/s13660-017-1349-4

  11. Guo, W.C., Lian, J.L., Wu, H.X.: The unified theory for the necessity of bounded commutators and applications. J. Geom. Anal. 30, 3995–4035 (2020)

    Article  MathSciNet  Google Scholar 

  12. Janson, S.: Mean oscillation and commutators of singular integral operators. Ark. Math. 16(1), 263–270 (1978)

    Article  MathSciNet  Google Scholar 

  13. Milman, M., Schonbek, T.: Second order estimates in interpolation theory and application. Proc. Am. Math. Soc. 110(4), 961–969 (1990)

    Article  MathSciNet  Google Scholar 

  14. O’Neil, R.: Fractional integration in Orlicz spaces. Trans. Am. Math. Soc. 115, 300–328 (1965)

    Article  MathSciNet  Google Scholar 

  15. Paluszyński, M.: Characterization of the Besov spaces via the commutator operator of Coifman, Rochberg and Weiss. Indiana Univ. Math. J. 44, 1–17 (1995)

    Article  MathSciNet  Google Scholar 

  16. Satorn, S.: Necessary and sufficient conditions for boundedness of commutators of fractional integral operators on classical Morrey spaces. Hokkaido Math. J. 35, 683–696 (2006)

    MathSciNet  Google Scholar 

  17. Shi, S.G., Lu, S.Z.: Some characterizations of Campanato spaces via commutators on Morrey spaces. Pac. J. Math. 264(1), 221–234 (2013)

    Article  MathSciNet  Google Scholar 

  18. Wang, D.H., Zhou, J.: Necessary and sufficient conditions for boundedness of commutators of bilinear Hardy–Littlewood maximal function (2017). arXiv:1708.09549v1 [math. FA]

  19. Zhang, L., Shi, S.G., Huang, H.: New characterizations of Lipshitz space via commutators on Morrey spaces. Adv. Math. (China) 44(6), 899–905 (2015)

    MathSciNet  MATH  Google Scholar 

  20. Zhang, P.: Characterization of Lipschitz spaces via commutators of the Hardy–Littlewood maximal function. C.R. Acad. Sci. Paris Ser. I 355, 336–344 (2017)

    Article  MathSciNet  Google Scholar 

  21. Zhang, P., Wu, J.L.: commutators for the maximal functions on Lebesgue spaces with variable exponent. Math. Inequal. Appl. 17(4), 1375–1386 (2014)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to thank the referees for their useful suggestions. This work was partially supported by Natural Science Foundation of Zhejiang Province (LQ21A010002) and by the National Natural Foundation of China (nos. 11701130, 11526067, and 51505295).

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Authors and Affiliations

  1. Department of Mathematics, Huzhou University, Huzhou, 313000, Zhejiang, People’s Republic of China

    Yun Fan

  2. School of Science, Hangzhou Dianzi University, Hangzhou, 310018, People’s Republic of China

    Guilian Gao

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  1. Yun Fan
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  2. Guilian Gao
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Correspondence to Guilian Gao.

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Communicated by Feng Dai.

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Fan, Y., Gao, G. Some characterizations of the generalized BMO spaces via the boundedness of maximal function commutators. Ann. Funct. Anal. 12, 25 (2021). https://doi.org/10.1007/s43034-021-00113-0

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  • DOI: https://doi.org/10.1007/s43034-021-00113-0

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