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Some characterizations of BMO spaces via commutators of maximal functions on Morrey-Lorentz spaces

Year 2025, Volume: 54 Issue: 5, 1845 - 1858, 29.10.2025
https://doi.org/10.15672/hujms.1579288

Abstract

In this paper, we investigate the commutators of the fractional maximal function and the sharp maximal function on Morrey-Lorentz spaces. Furthermore, we present some new characterizations of BMO spaces.

Supporting Institution

the National Natural Science Foundation of China

Project Number

12461021

References

  • [1] M. Agcayazi, A. Gogatishvili, K. Koca and R. Mustafayev, A note on maximal commutators and commutators of maximal functions, J. Math. Soc. Japan 67 (2), 581– 593, 2015.
  • [2] M. Agcayazi, A. Gogatishvili and R. Mustafayev, Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function, Tokyo J. Math. 41 (1), 193–218, 2018.
  • [3] C. Aykol, H. Armutcu and M. N. Omarova, Maximal commutator and commutator of maximal function on modified Morrey spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 36 (1), 29–35, 2016.
  • [4] J. Bastero, M. Milman and F. J. Ruiz, Commutators for the maximal and sharp functions, Proc. Am. Math. Soc. 128 (11), 3329–3334, 2000.
  • [5] R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (3), 611–635, 1976.
  • [6] N. A. Dao and S. G. Krantz, Lorentz boundedness and compactness characterization of integral commutators on spaces of homogeneous type, Nonlinear Anal. 203, 112162, 2021.
  • [7] N. A. Dao and S. G. Krantz, On the predual of a Morrey-Lorentz space and its applications to the linear Calderón-Zygmund operators, Front. Math. 19 (3), 385– 418, 2024.
  • [8] I. Ekincioglu, J. J. Hasanov and C. Keskin, On the boundedness of B-Riesz potential and its commutators on generalized weighted B-Morrey spaces, Hacet. J. Math. Stat. 53 (2), 321-332, 2024.
  • [9] C. Fefferman and E. M. Stein, $H_{p}$ spaces of several variables, Acta Math. 129, 137– 193, 1972.
  • [10] V. S. Guliyev, Commutators of the fractional maximal function in generalized Morrey spaces on Carnot groups, Complex Var. Elliptic 66 (6), 893–909, 2021.
  • [11] V. S. Guliyev, Some characterizations of BMO spaces via commutators in Orlicz spaces on stratified Lie groups, Results Math. 77 (1), 1–18, 2022.
  • [12] V. S. Guliyev, Maximal commutator and commutator of maximal function on total Morrey spaces, J. Math. Inequal, 16 (4), 1509-1524, 2022.
  • [13] V. S. Guliyev, Maximal commutator and commutator of maximal operator on Lorentz spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 44 (4), 1–7, 2024.
  • [14] V. S. Guliyev, F. Deringoz and S. G. Hasanov, Fractional maximal function and its commutators on Orlicz spaces, Anal. Math. Phys. 9, 165–179, 2019.
  • [15] N. Hatano, Fractional operators on Morrey-Lorentz spaces and the Olsen inequality, Math. Notes 107, 63–79, 2020.
  • [16] S. Janson, Mean oscillation and commutators of singular integral operators, Ark. Mat. 16 (1), 263–270, 1978.
  • [17] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (3), 415–426, 1961.
  • [18] G. G. Lorentz, On the theory of spaces $\Lambda$, Pacific J. Math. 1, 411–429, 1951.
  • [19] G. Lu, Bilinear Calderón-Zygmund operator and its commutator on some variable exponent spaces of homogeneous type, Hacet. J. Math. Stat. 53 (2), 433-456, 2024.
  • [20] M. Milman and T. Schonbek, Second order estimates in interpolation theory and applications, Proc. Am. Math. Soc. 110 (4), 961–969, 1990.
  • [21] M. A. Ragusa, Embeddings for Morrey-Lorentz spaces, J. Optim. Theory Appl. 154, 491–499, 2021.
  • [22] H. Yang and J. Zhou, Some characterizations of Lipschitz spaces via commutators of the Hardy-Littlewood maximal operator on slice spaces, Proc. Ro. Acad. Ser. A 24 (3), 223–230, 2023.
  • [23] H. Yang and J. Zhou, Compactness of commutators of fractional integral operators on ball Banach function spaces, AIMS Math. 9 (2), 3126–3149, 2024.
  • [24] H. Yang and J. Zhou, Commutators of some maximal functions with Lipschitz functions on mixed Morrey spaces, Filomat 38 (31), 11031–11043, 2024.
  • [25] X. Yang, Z. Yang and B. Li, Characterization of Lipschitz space via the commutators of fractional maximal functions on variable lebesgue spaces, Potential Anal. 60 (2), 703–720, 2024.
  • [26] P. Zhang and J. Wu, Commutators of the fractional maximal functions, Acta Math. Sin. 52 (6), 1235–1238, 2009.
  • [27] P. Zhang and J. Wu, Commutators of the fractional maximal function on variable exponent Lebesgue spaces, Czech. Math. J. 64 (1), 183–197, 2014.
  • [28] P. Zhang, J. Wu and J. Sun, Commutators of some maximal functions with Lipschitz function on Orlicz spaces, Mediterr. J. Math. 15, 1–13, 2018.

Year 2025, Volume: 54 Issue: 5, 1845 - 1858, 29.10.2025
https://doi.org/10.15672/hujms.1579288

Abstract

Project Number

12461021

References

  • [1] M. Agcayazi, A. Gogatishvili, K. Koca and R. Mustafayev, A note on maximal commutators and commutators of maximal functions, J. Math. Soc. Japan 67 (2), 581– 593, 2015.
  • [2] M. Agcayazi, A. Gogatishvili and R. Mustafayev, Weak-type estimates in Morrey spaces for maximal commutator and commutator of maximal function, Tokyo J. Math. 41 (1), 193–218, 2018.
  • [3] C. Aykol, H. Armutcu and M. N. Omarova, Maximal commutator and commutator of maximal function on modified Morrey spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 36 (1), 29–35, 2016.
  • [4] J. Bastero, M. Milman and F. J. Ruiz, Commutators for the maximal and sharp functions, Proc. Am. Math. Soc. 128 (11), 3329–3334, 2000.
  • [5] R. R. Coifman, R. Rochberg and G. Weiss, Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (3), 611–635, 1976.
  • [6] N. A. Dao and S. G. Krantz, Lorentz boundedness and compactness characterization of integral commutators on spaces of homogeneous type, Nonlinear Anal. 203, 112162, 2021.
  • [7] N. A. Dao and S. G. Krantz, On the predual of a Morrey-Lorentz space and its applications to the linear Calderón-Zygmund operators, Front. Math. 19 (3), 385– 418, 2024.
  • [8] I. Ekincioglu, J. J. Hasanov and C. Keskin, On the boundedness of B-Riesz potential and its commutators on generalized weighted B-Morrey spaces, Hacet. J. Math. Stat. 53 (2), 321-332, 2024.
  • [9] C. Fefferman and E. M. Stein, $H_{p}$ spaces of several variables, Acta Math. 129, 137– 193, 1972.
  • [10] V. S. Guliyev, Commutators of the fractional maximal function in generalized Morrey spaces on Carnot groups, Complex Var. Elliptic 66 (6), 893–909, 2021.
  • [11] V. S. Guliyev, Some characterizations of BMO spaces via commutators in Orlicz spaces on stratified Lie groups, Results Math. 77 (1), 1–18, 2022.
  • [12] V. S. Guliyev, Maximal commutator and commutator of maximal function on total Morrey spaces, J. Math. Inequal, 16 (4), 1509-1524, 2022.
  • [13] V. S. Guliyev, Maximal commutator and commutator of maximal operator on Lorentz spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 44 (4), 1–7, 2024.
  • [14] V. S. Guliyev, F. Deringoz and S. G. Hasanov, Fractional maximal function and its commutators on Orlicz spaces, Anal. Math. Phys. 9, 165–179, 2019.
  • [15] N. Hatano, Fractional operators on Morrey-Lorentz spaces and the Olsen inequality, Math. Notes 107, 63–79, 2020.
  • [16] S. Janson, Mean oscillation and commutators of singular integral operators, Ark. Mat. 16 (1), 263–270, 1978.
  • [17] F. John and L. Nirenberg, On functions of bounded mean oscillation, Comm. Pure Appl. Math. 14 (3), 415–426, 1961.
  • [18] G. G. Lorentz, On the theory of spaces $\Lambda$, Pacific J. Math. 1, 411–429, 1951.
  • [19] G. Lu, Bilinear Calderón-Zygmund operator and its commutator on some variable exponent spaces of homogeneous type, Hacet. J. Math. Stat. 53 (2), 433-456, 2024.
  • [20] M. Milman and T. Schonbek, Second order estimates in interpolation theory and applications, Proc. Am. Math. Soc. 110 (4), 961–969, 1990.
  • [21] M. A. Ragusa, Embeddings for Morrey-Lorentz spaces, J. Optim. Theory Appl. 154, 491–499, 2021.
  • [22] H. Yang and J. Zhou, Some characterizations of Lipschitz spaces via commutators of the Hardy-Littlewood maximal operator on slice spaces, Proc. Ro. Acad. Ser. A 24 (3), 223–230, 2023.
  • [23] H. Yang and J. Zhou, Compactness of commutators of fractional integral operators on ball Banach function spaces, AIMS Math. 9 (2), 3126–3149, 2024.
  • [24] H. Yang and J. Zhou, Commutators of some maximal functions with Lipschitz functions on mixed Morrey spaces, Filomat 38 (31), 11031–11043, 2024.
  • [25] X. Yang, Z. Yang and B. Li, Characterization of Lipschitz space via the commutators of fractional maximal functions on variable lebesgue spaces, Potential Anal. 60 (2), 703–720, 2024.
  • [26] P. Zhang and J. Wu, Commutators of the fractional maximal functions, Acta Math. Sin. 52 (6), 1235–1238, 2009.
  • [27] P. Zhang and J. Wu, Commutators of the fractional maximal function on variable exponent Lebesgue spaces, Czech. Math. J. 64 (1), 183–197, 2014.
  • [28] P. Zhang, J. Wu and J. Sun, Commutators of some maximal functions with Lipschitz function on Orlicz spaces, Mediterr. J. Math. 15, 1–13, 2018.
There are 28 citations in total.

Details

Primary Language English
Subjects Lie Groups, Harmonic and Fourier Analysis
Journal Section Research Article
Authors

Heng Yang This is me 0009-0009-5130-9503

Jiang Zhou 0000-0003-1541-5316

Project Number 12461021
Early Pub Date April 11, 2025
Publication Date October 29, 2025
Submission Date November 5, 2024
Acceptance Date February 14, 2025
Published in Issue Year 2025 Volume: 54 Issue: 5

Cite

APA Yang, H., & Zhou, J. (2025). Some characterizations of BMO spaces via commutators of maximal functions on Morrey-Lorentz spaces. Hacettepe Journal of Mathematics and Statistics, 54(5), 1845-1858. https://doi.org/10.15672/hujms.1579288
AMA Yang H, Zhou J. Some characterizations of BMO spaces via commutators of maximal functions on Morrey-Lorentz spaces. Hacettepe Journal of Mathematics and Statistics. October 2025;54(5):1845-1858. doi:10.15672/hujms.1579288
Chicago Yang, Heng, and Jiang Zhou. “Some Characterizations of BMO Spaces via Commutators of Maximal Functions on Morrey-Lorentz Spaces”. Hacettepe Journal of Mathematics and Statistics 54, no. 5 (October 2025): 1845-58. https://doi.org/10.15672/hujms.1579288.
EndNote Yang H, Zhou J (October 1, 2025) Some characterizations of BMO spaces via commutators of maximal functions on Morrey-Lorentz spaces. Hacettepe Journal of Mathematics and Statistics 54 5 1845–1858.
IEEE H. Yang and J. Zhou, “Some characterizations of BMO spaces via commutators of maximal functions on Morrey-Lorentz spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 5, pp. 1845–1858, 2025, doi: 10.15672/hujms.1579288.
ISNAD Yang, Heng - Zhou, Jiang. “Some Characterizations of BMO Spaces via Commutators of Maximal Functions on Morrey-Lorentz Spaces”. Hacettepe Journal of Mathematics and Statistics 54/5 (October2025), 1845-1858. https://doi.org/10.15672/hujms.1579288.
JAMA Yang H, Zhou J. Some characterizations of BMO spaces via commutators of maximal functions on Morrey-Lorentz spaces. Hacettepe Journal of Mathematics and Statistics. 2025;54:1845–1858.
MLA Yang, Heng and Jiang Zhou. “Some Characterizations of BMO Spaces via Commutators of Maximal Functions on Morrey-Lorentz Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 5, 2025, pp. 1845-58, doi:10.15672/hujms.1579288.
Vancouver Yang H, Zhou J. Some characterizations of BMO spaces via commutators of maximal functions on Morrey-Lorentz spaces. Hacettepe Journal of Mathematics and Statistics. 2025;54(5):1845-58.