[1] Alvarez, J., Lakey, J., Guzmán-Partida, M.: Spaces of bounded $\lambda$-central mean oscillation, Morrey spaces, and $\lambda$-central Carleson measures. Collect. Math. 51 (2000), 1-47. MR 1757848 | Zbl 0948.42013

[2] Capone, C., Cruz-Uribe, D., Fiorenza, A.: The fractional maximal operator and fractional integrals on variable $L^p$ spaces. Rev. Mat. Iberoam. 23 (2007), 743-770. DOI 10.4171/RMI/511 | MR 2414490 | Zbl 1213.42063

[3] Christ, M., Grafakos, L.: Best constants for two nonconvolution inequalities. Proc. Am. Math. Soc. 123 (1995), 1687-1693. DOI 10.1090/S0002-9939-1995-1239796-6 | MR 1239796 | Zbl 0830.42009

[4] Cruz-Uribe, D., Fiorenza, A., Neugebauer, C. J.: The maximal function on variable $L^p$ spaces. Ann. Acad. Sci. Fenn., Math. 28 (2003), 223-238. MR 1976842 | Zbl 1037.42023

[5] Cruz-Uribe, D., Wang, D.: Variable Hardy spaces. Indiana Univ. Math. J. 63 (2014), 447-493. DOI 10.1512/iumj.2014.63.5232 | MR 3233216 | Zbl 1311.42053

[6] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics 2017. Springer, Berlin (2011). DOI 10.1007/978-3-642-18363-8 | MR 2790542 | Zbl 1222.46002

[7] Fu, Z. W., Gong, S. L., Lu, S. Z., Yuan, W.: Weighted multilinear Hardy operators and commutators. Forum Math. 27 (2015), 2825-2851. DOI 10.1515/forum-2013-0064 | MR 3393380 | Zbl 1331.42016

[8] Fu, Z., Lin, Y.: $\lambda$-central BMO estimates for commutators of higher dimensional fractional Hardy operators. Acta Math. Sin., Chin. Ser. 53 (2010), 925-932 Chinese. DOI 10.12386/A2010sxxb0103 | MR 2722928 | Zbl 1240.42040

[9] Fu, Z., Liu, Z., Lu, S., Wang, H.: Characterization for commutators of $n$-dimensional fractional Hardy operators. Sci. China, Ser. A 50 (2007), 1418-1426. DOI 10.1007/s11425-007-0094-4 | MR 2390459 | Zbl 1131.42012

[10] Fu, Z., Lu, S., Shi, S.: Two characterizations of central BMO space via the commutators of Hardy operators. Forum Math. 33 (2021), 505-529. DOI 10.1515/forum-2020-0243 | MR 4223073 | Zbl 1491.42035

[11] Fu, Z., Lu, S., Wang, H., Wang, L.: Singular integral operators with rough kernels on central Morrey spaces with variable exponent. Ann. Acad. Sci. Fenn., Math. 44 (2019), 505-522. DOI 10.5186/aasfm.2019.4431 | MR 3919152 | Zbl 1412.42059

[12] Fu, Z., Lu, S., Zhao, F.: Commutators of $n$-dimensional rough Hardy operators. Sci. China, Math. 54 (2011), 95-104. DOI 10.1007/s11425-010-4110-8 | MR 2764788 | Zbl 1226.47050

[13] Hardy, G. H.: Note on a theorem of Hilbert. Math. Z. 6 (1920), 314-317 \99999JFM99999 47.0207.01. DOI 10.1007/BF01199965 | MR 1544414

[14] Harjulehto, P., Hästö, P., Lê, Ú. V., Nuortio, M.: Overview of differential equations with non-standard growth. Nonlinear Anal., Theory Methods Appl., Ser. A 72 (2010), 4551-4574. DOI 10.1016/j.na.2010.02.033 | MR 2639204 | Zbl 1188.35072

[15] Ho, K.-P.: Hardy's inequality on Hardy-Morrey spaces with variable exponents. Mediterr. J. Math. 14 (2017), Article ID 79, 19 pages. DOI 10.1007/s00009-016-0811-8 | MR 3620157 | Zbl 1367.26034

[16] Hussain, A., Asim, M., Jarad, F.: Variable $\lambda$-central Morrey space estimates for the fractional Hardy operators and commutators. J. Math. 2022 (2022), Article ID 5855068, 12 pages. DOI 10.1155/2022/5855068 | MR 4425886

[17] Izuki, M.: Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization. Anal. Math. 36 (2010), 33-50. DOI 10.1007/s10476-010-0102-8 | MR 2606575 | Zbl 1224.42025

[18] Kováčik, O., Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k,p(x)}$. Czech. Math. J. 41 (1991), 592-618. DOI 10.21136/CMJ.1991.102493 | MR 1134951 | Zbl 0784.46029

[19] Mizuta, Y., Nekvinda, A., Shimomura, T.: Optimal estimates for the fractional Hardy operator. Stud. Math. 227 (2015), 1-19. DOI 10.4064/sm227-1-1 | MR 3359954 | Zbl 1328.47049

[20] Mizuta, Y., Ohno, T., Shimomura, T.: Boundedness of maximal operators and Sobolev's theorem for non-homogeneous central Morrey spaces of variable exponent. Hokkaido Math. J. 44 (2015), 185-201. DOI 10.14492/hokmj/1470053290 | MR 3532106 | Zbl 1334.31004

[21] Nakai, E., Sawano, Y.: Hardy spaces with variable exponents and generalized Campanato spaces. J. Funct. Anal. 262 (2012), 3665-3748. DOI 10.1016/j.jfa.2012.01.004 | MR 2899976 | Zbl 1244.42012

[22] Orlicz, W.: Über konjugierte Exponentenfolgen. Stud. Math. 3 (1931), 200-212 German. DOI 10.4064/sm-3-1-200-211 | Zbl 0003.25203

[23] Růžička, M.: Electrorheological Fluids: Modeling and Mathematical Theory. Lecture Notes in Mathematics 1748. Springer, Berlin (2000). DOI 10.1007/BFb0104029 | MR 1810360 | Zbl 0962.76001

[24] Shi, S., Fu, Z., Lu, S.: On the compactness of commutators of Hardy operators. Pac. J. Math. 307 (2020), 239-256. DOI 10.2140/pjm.2020.307.239 | MR 4131808 | Zbl 1445.42015

[25] Shi, S., Lu, S.: Characterization of the central Campanato space via the commutator operator of Hardy type. J. Math. Anal. Appl. 429 (2015), 713-732. DOI 10.1016/j.jmaa.2015.03.083 | MR 3342488 | Zbl 1317.42022

[26] Tan, J., Liu, Z.: Some boundedness of homogeneous fractional integrals on variable exponent function spaces. Acta Math. Sin., Chin. Ser. 58 (2015), 309-320 Chinese. DOI 10.12386/A2015sxxb0030 | MR 3408398 | Zbl 1340.42055

[27] Tan, J., Liu, Z., Zhao, J.: On some multilinear commutators in variable Lebesgue spaces. J. Math. Inequal. 11 (2017), 715-734. DOI 10.7153/jmi-2017-11-57 | MR 3732810 | Zbl 1375.42033

[28] Torchinsky, A.: Real-Variable Methods in Harmonic Analysis. Pure and Applied Mathematics 123. Academic Press, New York (1986). MR 0869816 | Zbl 0621.42001

[29] Wang, H.: Commutators of Marcinkiewicz integrals on Herz spaces with variable exponent. Czech. Math. J. 66 (2016), 251-269. DOI 10.1007/s10587-016-0254-1 | MR 3483237 | Zbl 1413.42029

[30] Wang, H.: The continuity of commutators on Herz-type Hardy spaces with variable exponent. Kyoto J. Math. 56 (2016), 559-573. DOI 10.1215/21562261-3600175 | MR 3542775 | Zbl 1348.42014

[31] Wang, H.: Commutators of singular integral operator on Herz-type Hardy spaces with variable exponent. J. Korean Math. Soc. 54 (2017), 713-732. DOI 10.4134/JKMS.j150771 | MR 3640903 | Zbl 1366.42018

[32] Wang, H., Fu, Z.: Estimates of commutators on Herz-type spaces with variable exponent and applications. Banach J. Math. Anal. 15 (2021), Article ID 36, 27 pages. DOI 10.1007/s43037-021-00120-2 | MR 4216372 | Zbl 1470.42027

[33] Wang, H., Liao, F.: Boundedness of singular integral operators on Herz-Morrey spaces with variable exponent. Chin. Ann. Math., Ser. B 41 (2020), 99-116. DOI 10.1007/s11401-019-0188-7 | MR 4036493 | Zbl 1431.42031

[34] Wang, H., Liu, Z.: Boundedness of singular integral operators on weak Herz type spaces with variable exponent. Ann. Funct. Anal. 11 (2020), 1108-1125. DOI 10.1007/s43034-020-00075-9 | MR 4133617 | Zbl 1446.42036

[35] Wang, H., Xu, J.: Multilinear fractional integral operators on central Morrey spaces with variable exponent. J. Inequal. Appl. 2019 (2019), Article ID 311, 23 pages. DOI 10.1186/s13660-019-2264-7 | MR 4062057 | Zbl 1499.42116

[36] Wang, H., Xu, J., Tan, J.: Boundedness of multilinear singular integrals on central Morrey spaces with variable exponents. Front. Math. China 15 (2020), 1011-1034. DOI 10.1007/s11464-020-0864-7 | MR 4173409 | Zbl 1472.42024

[37] Wang, L.: Multilinear Calderón-Zygmund operators and their commutators on central Morrey spaces with variable exponent. Bull. Korean Math. Soc. 57 (2020), 1427-1449. DOI 10.4134/BKMS.b191108 | MR 4180187 | Zbl 1462.42026

[38] Wu, Q. Y., Fu, Z. W.: Weighted $p$-adic Hardy operators and their commutators on $p$-adic central Morrey spaces. Bull. Malays. Math. Sci. Soc. (2) 40 (2017), 635-654. DOI 10.1007/s40840-017-0444-5 | MR 3620272 | Zbl 1407.42009

[39] Xu, J.: Variable Besov and Triebel-Lizorkin spaces. Ann. Acad. Sci. Fenn., Math. 33 (2008), 511-522. MR 2431378 | Zbl 1160.46025

[40] Yang, D., Yuan, W., Zhuo, C.: Triebel-Lizorkin type spaces with variable exponents. Banach J. Math. Anal. 9 (2015), 146-202. DOI 10.15352/bjma/09-4-9 | MR 3336888 | Zbl 1339.46040

[41] Yang, D., Zhuo, C., Yuan, W.: Besov-type spaces with variable smoothness and integrability. J. Funct. Anal. 269 (2015), 1840-1898. DOI 10.1016/j.jfa.2015.05.016 | MR 3373435 | Zbl 1342.46038

[42] Zhao, F., Fu, Z., Lu, S.: $M_p$ weights for bilinear Hardy operators on $\Bbb{R}^n$. Collect. Math. 65 (2014), 87-102. DOI 10.1007/s13348-013-0083-6 | MR 3147771 | Zbl 1305.26042