Some characterizations of the generalized BMO spaces via the boundedness of maximal function commutators. (English) Zbl 1457.42035
Summary: 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.
MSC:
| 42B30 | \(H^p\)-spaces |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B35 | Function spaces arising in harmonic analysis |
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) · Zbl 1330.42012 · doi:10.2969/jmsj/06720581 |
| [2] | Bastero, J.; Milman, M.; Ruiz, FJ, Commutators of the maximal and sharp functions, Proc. Am. Math. Soc., 128, 11, 3329-3334 (2000) · Zbl 0957.42010 · doi:10.1090/S0002-9939-00-05763-4 |
| [3] | Coifman, RR; Rochberg, R.; Weiss, G., Factorization theorems for Hardy spaces in several variable, Ann. Math., 103, 3, 611-635 (1976) · Zbl 0326.32011 · doi:10.2307/1970954 |
| [4] | Deringoz, F.; Guliyev, VS; Hasanov, SG, Characterizations for the Riesz potential and its commutators on generalized Orlicz-Morrey spaces, J. Inequal. Appl. (2016) · Zbl 1348.42013 · doi:10.1186/s13660-016-1192-z |
| [5] | Deringoz, F.; Guliyev, VS; 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) · Zbl 1318.42015 |
| [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) · Zbl 1401.42018 · doi:10.3836/tjm/1502179258 |
| [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. doi:10.1155/2014/617414 · Zbl 1472.42038 |
| [9] | Guliyev, VS; Deringoz, F., Some characterizations of Lipschitz spaces via commutators on generalized Orlicz-Morrey spaces, Mediterr. J. Math., 15, 4, 180 (2018) · Zbl 1400.42025 · doi:10.1007/s00009-018-1226-5 |
| [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). doi:10.1186/s13660-017-1349-4 · Zbl 1364.31005 |
| [11] | Guo, WC; Lian, JL; Wu, HX, The unified theory for the necessity of bounded commutators and applications, J. Geom. Anal., 30, 3995-4035 (2020) · Zbl 1475.42024 · doi:10.1007/s12220-019-00226-y |
| [12] | Janson, S., Mean oscillation and commutators of singular integral operators, Ark. Math., 16, 1, 263-270 (1978) · Zbl 0404.42013 · doi:10.1007/BF02386000 |
| [13] | Milman, M.; Schonbek, T., Second order estimates in interpolation theory and application, Proc. Am. Math. Soc., 110, 4, 961-969 (1990) · Zbl 0717.46066 · doi:10.1090/S0002-9939-1990-1075187-4 |
| [14] | O’Neil, R., Fractional integration in Orlicz spaces, Trans. Am. Math. Soc., 115, 300-328 (1965) · Zbl 0132.09201 · doi:10.1090/S0002-9947-1965-0194881-0 |
| [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) · Zbl 0838.42006 · doi:10.1512/iumj.1995.44.1976 |
| [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) · Zbl 1122.42007 · doi:10.14492/hokmj/1285766424 |
| [17] | Shi, SG; Lu, SZ, Some characterizations of Campanato spaces via commutators on Morrey spaces, Pac. J. Math., 264, 1, 221-234 (2013) · Zbl 1273.42015 · doi:10.2140/pjm.2013.264.221 |
| [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, SG; Huang, H., New characterizations of Lipshitz space via commutators on Morrey spaces, Adv. Math. (China), 44, 6, 899-905 (2015) · Zbl 1349.42040 |
| [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) · Zbl 1364.42026 · doi:10.1016/j.crma.2017.01.022 |
| [21] | Zhang, P.; Wu, JL, commutators for the maximal functions on Lebesgue spaces with variable exponent, Math. Inequal. Appl., 17, 4, 1375-1386 (2014) · Zbl 1305.42024 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
