Article
| Title: | Boundedness of singular integral operators on generalized two-weight Morrey spaces (English) |
| Author: | Lv, Meichuan |
| Author: | Li, Wenming |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 1 |
| Year: | 2026 |
| Pages: | 151-176 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the boundedness of the Hardy-Littlewood maximal operator, the Calderón-Zygmund singular integral operators and the commutators of the singular integral operators with BMO functions on the generalized two-weight Morrey spaces. We also obtain the endpoint estimates for these operators. (English) |
| Keyword: | generalized two-weighted Morrey space |
| Keyword: | Hardy-Littlewood maximal operator |
| Keyword: | Calderón-Zygmund singular integral operator |
| Keyword: | commutator |
| MSC: | 42B20 |
| MSC: | 42B25 |
| DOI: | 10.21136/CMJ.2026.0206-25 |
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| Date available: | 2026-03-13T09:31:11Z |
| Last updated: | 2026-03-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153566 |
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| Reference: | [1] Alvarez, J., Pérez, C.: Estimates with $A_\infty$ weights for various singular integral operators.Boll. Unione Mat. Ital., VII. Ser., A 8 (1994), 123-133. Zbl 0807.42013, MR 1273194 |
| Reference: | [2] Bennett, C., Sharppley, R.: Interpolation of Operators.Pure and Applied Mathematics 129. Academic Press, Boston (1988). Zbl 0647.46057, MR 0928802, 10.1016/s0079-8169(08)x6053-2 |
| Reference: | [3] Chiarenza, F., Frasca, M.: Morrey spaces and Hardy-Littlewood maximal function.Rend. Math. Appl., VII. Ser. 7 (1987), 273-279. Zbl 0717.42023, MR 0985999 |
| Reference: | [4] Cruz-Uribe, D., Martell, J. M., Pérez, C.: Extrapolation from $A_\infty$ weights and applications.J. Funct. Anal. 213 (2004), 412-439. Zbl 1052.42016, MR 2078632, 10.1016/j.jfa.2003.09.002 |
| Reference: | [5] Cruz-Uribe, D., Martell, J. M., Pérez, C.: Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture.Adv. Math. 216 (2007), 647-676. Zbl 1129.42007, MR 2351373, 10.1016/j.aim.2007.05.022 |
| Reference: | [6] Cruz-Uribe, D., Martell, J. M., Pérez, C.: Weights, Extrapolation and the Theory of Rubio de Francia.Operator Theory: Advances and Applications 215. Birkhäuser, Basel (2011). Zbl 1234.46003, MR 2797562, 10.1007/978-3-0348-0072-3 |
| Reference: | [7] Cruz-Uribe, D., Pérez, C.: Sharp two-weight, weak-type norm inequalities for singular integral operators.Math. Res. Lett. 6 (1999), 417-427. Zbl 0961.42013, MR 1713140, 10.4310/MRL.1999.v6.n4.a4 |
| Reference: | [8] Cruz-Uribe, D., Pérez, C.: On the two-weight problem for singular integral operators.Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 1 (2002), 821-849. Zbl 1072.42010, MR 1991004 |
| Reference: | [9] Duoandikoetxea, J., Rosenthal, M.: Boundedness properties in a family of weighted Morrey spaces with emphasis on power weights.J. Funct. Anal. 279 (2020), Article ID 108687, 26 pages. Zbl 1451.42027, MR 4116151, 10.1016/j.jfa.2020.108687 |
| Reference: | [10] García-Cuerva, J., Francia, J. L. Rubio de: Weighted Norm Inequalities and Related Topics.North-Holland Mathematics Studies 116. North-Holland, Amsterdam (1985). Zbl 0578.46046, MR 0807149, 10.1016/s0304-0208(08)x7154-3 |
| Reference: | [11] Grafakos, L.: Modern Fourier Analysis.Graduate Texts in Mathematics 250. Springer, New York (2009). Zbl 1158.42001, MR 2463316, 10.1007/978-0-387-09434-2 |
| Reference: | [12] Ho, K.-P.: Two-weight norm, Poincaré, Sobolev and Stein-Weiss inequalities on Morrey spaces.Publ. Res. Inst. Math. Sci. 53 (2017), 119-139. Zbl 1366.26023, MR 3615043, 10.4171/PRIMS/53-1-4 |
| Reference: | [13] Ho, K.-P.: Weak type estimates of singular integral operators on Morrey-Banach spaces.Integral Equations Oper. Theory 91 (2019), Article ID 20, 18 pages. Zbl 1418.42018, MR 3937930, 10.1007/s00020-019-2517-3 |
| Reference: | [14] Ho, K.-P.: Definability of singular integral operators on Morrey-Banach spaces.J. Math. Soc. Japan 72 (2020), 155-170. Zbl 1437.42016, MR 4055093, 10.2969/jmsj/81208120 |
| Reference: | [15] Ho, K.-P.: Potential type operators on weighted Morrey spaces.Arch. Math. 118 (2022), 159-168. Zbl 1491.42021, MR 4386871, 10.1007/s00013-021-01685-y |
| Reference: | [16] Ho, K.-P.: Two-weight norm inequalities for rough fractional integral operators on Morrey spaces.Opusc. Math. 44 (2024), 67-77. Zbl 1527.42016, MR 4664674, 10.7494/OpMath.2024.44.1.67 |
| Reference: | [17] Iida, T.: The boundedness of the Hardy-Littlewood maximal operator and multilinear maximal operator in weighted Morrey type spaces.J. Funct. Spaces 2014 (2014), Article ID 648251, 8 pages. Zbl 1286.42027, MR 3187059, 10.1155/2014/648251 |
| Reference: | [18] Komori, Y., Shirai, S.: Weighted Morrey spaces and a singular integral operator.Math. Nachr. 282 (2009), 219-231. Zbl 1160.42008, MR 2493512, 10.1002/mana.200610733 |
| Reference: | [19] Lv, M., Li, W.: Singular integral operators and commutators on two-weight Morrey spaces.Math. Nachr. 298 (2025), 1713-1726. Zbl 08041125, MR 4904186, 10.1002/mana.12007 |
| Reference: | [20] Muckenhoupt, B.: Weighted norm inequalities for the Hardy maximal function.Trans. Am. Math. Soc. 165 (1972), 207-226. Zbl 0236.26016, MR 0293384, 10.1090/S0002-9947-1972-0293384-6 |
| Reference: | [22] Nakamura, S., Sawano, Y.: The singular integral operator and its commutator on weighted Morrey spaces.Collect. Math. 68 (2017), 145-174. Zbl 1375.42020, MR 3633056, 10.1007/s13348-017-0193-7 |
| Reference: | [23] Nakamura, S., Sawano, Y., Tanaka, H.: Weighted local Morrey spaces.Ann. Acad. Sci. Fenn., Math. 45 (2020), 67-93. Zbl 1437.42024, MR 4056529, 10.5186/aasfm.2020.4504 |
| Reference: | [24] Neugebauer, C. J.: Inserting $A_p$-weights.Proc. Am. Math. Soc. 87 (1983), 644-648. Zbl 0521.42019, MR 0687633, 10.1090/S0002-9939-1983-0687633-2 |
| Reference: | [21] O'Neil, R.: Fractional integration in Orlicz spaces. I.Trans. Am. Math. Soc. 115 (1965), 300-328. Zbl 0132.09201, MR 0194881, 10.1090/S0002-9947-1965-0194881-0 |
| Reference: | [25] Pérez, C.: Endpoint estimates for commutators of singular integral operators.J. Funct. Anal. 128 (1995), 163-185. Zbl 0831.42010, MR 1317714, 10.1006/jfan.1995.1027 |
| Reference: | [26] Pérez, C.: On sufficient conditions for the boundedness of the Hardy-Littlewood maximal operator between weighted $L^p$-spaces with different weights.Proc. Lond. Math. Soc., III. Ser. 71 (1995), 135-157. Zbl 0829.42019, MR 1327936, 10.1112/plms/s3-71.1.135 |
| Reference: | [27] Pérez, C.: Sharp estimates for commutators of singular integrals via iterations of the Hardy-Littlewood maximal function.J. Fourier Anal. Appl. 3 (1997), 743-756. Zbl 0894.42006, MR 1481632, 10.1007/BF02648265 |
| Reference: | [28] Pérez, C., Pradolini, G.: Sharp weighted endpoint estimates for commutators of singular integrals.Mich. Math. J. 49 (2001), 23-37. Zbl 1010.42007, MR 1827073, 10.1307/mmj/1008719033 |
| Reference: | [29] Qi, J., Shi, H., Li, W.: Weighted endpoint estimates for commutators of singular integral operators on Orlicz-Morrey spaces.J. Funct. Spaces 2019 (2019), Article ID 5458101, 6 pages. Zbl 1416.42023, MR 3924139, 10.1155/2019/5458101 |
| Reference: | [30] Samko, N.: Weighted Hardy and singular operators in Morrey spaces.J. Math. Anal. Appl. 350 (2009), 56-72. Zbl 1155.42005, MR 2476892, 10.1016/j.jmaa.2008.09.021 |
| Reference: | [31] Sawyer, E. T.: A characterization of a two-weight norm inequality for maximal operators.Stud. Math. 75 (1982), 1-11. Zbl 0508.42023, MR 0676801, 10.4064/sm-75-1-1-11 |
| Reference: | [32] Tanaka, H.: Two-weight norm inequalities on Morrey spaces.Ann. Acad. Sci. Fenn., Math. 40 (2015), 773-791. Zbl 1331.42023, MR 3409703, 10.5186/aasfm.2015.4042 |
| Reference: | [33] Wang, H.: Boundedness of fractional integral operators with rough kernels on weighted Morrey spaces.Acta Math. Sin., Chin. Ser. 56 (2013), 175-186 Chinese. Zbl 1289.42057, MR 3097397, 10.12386/A2013sxxb0018 |
| Reference: | [34] Ye, X., Wang, T.: Two-weighted norm inequality on weighted Morrey spaces.Turk. J. Math. 38 (2014), 426-435. Zbl 1296.42013, MR 3178125, 10.3906/mat-1304-18 |
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